Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations | Paper Citation Record

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

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Observation bfa3aac4-2806-44e0-a0dd-92849ea15f01 · outbound

This paper cites ( A9-A11) and the addition of multiples of the left-hand sides of Eqs.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations ( A9-A11) and the addition of multiples of the left-hand sides of Eqs

Reference 3

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This paper cites Furthermore, one can use the hatted transformations to achieve π1 = π2 = 0 and κ1 = 0.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Furthermore, one can use the hatted transformations to achieve π1 = π2 = 0 and κ1 = 0

Reference 4

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This paper cites sufﬁciently regular.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations sufﬁciently regular

Reference 5

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 6

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Observation c9397e75-3d90-49aa-becf-09b1178ddd01 · outbound

This paper cites Chabanov, L.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Chabanov, L

Reference 7

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

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Observation 57526a77-4f86-4a9a-9425-a5f94f227102 · outbound

This paper cites V´ an, Nonequilibrium thermody- namics: emergent and fundamental, Philosophical Transactions of the Royal Society A: Mathema tical, Physical and.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations V´ an, Nonequilibrium thermody- namics: emergent and fundamental, Philosophical Transactions of the Royal Society A: Mathema tical, Physical and

Reference 9

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This paper cites Explicitly, they are given by µ1,2 = 1 2 Ä T r ± √ T r2 − 4D ä , (103) where D = 1 d kBT e , T r = 1 d + kBT e Å 1 + A0 κ ã.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Explicitly, they are given by µ1,2 = 1 2 Ä T r ± √ T r2 − 4D ä , (103) where D = 1 d kBT e , T r = 1 d + kBT e Å 1 + A0 κ ã

Reference 11

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 12

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 13

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Observation 5b14f45c-7973-441c-bdb3-3c12e2c39e19 · outbound

This paper cites In particular, V = 0 is the unique solution with trivial initial data, and hence the constraints propag ate as desired.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations In particular, V = 0 is the unique solution with trivial initial data, and hence the constraints propag ate as desired

Reference 14

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Observation fbc17d2c-7ef2-479c-8d83-bc2be4fa3ed4 · outbound

This paper cites Kovtun, First-order relativistic hydrodynamics is stab le, JHEP 10, 034.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Kovtun, First-order relativistic hydrodynamics is stab le, JHEP 10, 034

Reference 15

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Observation 1b906d8b-81b3-492f-8911-341d66739773 · outbound

This paper cites A speciﬁc choice is referred to as a “frame” in the literature.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations A speciﬁc choice is referred to as a “frame” in the literature

Reference 16

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 17

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 18

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 19

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Observation 17c92979-8e64-41f0-a7e4-e5812cf5c303 · outbound

This paper cites time evolution vector ﬁeld.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations time evolution vector ﬁeld

Reference 20

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This paper cites In contrast , we ﬁrst perform a change of frame before adding these combina- tions.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations In contrast , we ﬁrst perform a change of frame before adding these combina- tions

Reference 21

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Observation 2dc6c0b7-eb1b-4f32-9fe6-788216acda29 · outbound

This paper cites In order to do so we deﬁne A µ := uµI − Aµ(U ) with I denoting the identity ma- trix and the matrices Aµ(U ) satisfying Aµ(U )uµ = 0.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations In order to do so we deﬁne A µ := uµI − Aµ(U ) with I denoting the identity ma- trix and the matrices Aµ(U ) satisfying Aµ(U )uµ = 0

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.983661Z

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 23

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Observation bb0dd2ef-c0df-435e-94af-e9d7b673666b · outbound

This paper cites Derradi de Souza, T.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Derradi de Souza, T

Reference 24

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This paper cites Du and U.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Du and U

Reference 25

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Observation 5e30f3c9-be06-4c3a-9649-7c4145f5f25f · outbound

This paper cites Shen and L.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Shen and L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.938784Z

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 27

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 28

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Observation 0153a4ff-dc82-44f5-988e-034fde1bd155 · outbound

This paper cites Hawking and G.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Hawking and G

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.652791Z

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 30

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 31

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Observation 77fa5a4f-5791-4155-9772-d6721ecaa7df · outbound

This paper cites Abalos and O.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Abalos and O

Reference 32

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Observation cd3c369a-62bf-4c5e-8325-9f535f14b486 · outbound

This paper cites Gavassino and M.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Gavassino and M

Reference 33

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Observation 333e2103-8093-4c15-b90d-590ae6cc6779 · outbound

This paper cites Hyperbolic extensions of constrained PDEs.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Hyperbolic extensions of constrained PDEs

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-11T22:21:43.384762Z

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Observation dc5f9074-4e43-4ead-b15a-2e74c3fc8f5c · outbound

This paper cites Partial Differential Equations of Physics.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Partial Differential Equations of Physics

Reference 35

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Observation 0a1d4f76-8510-4aab-a3be-96d417be77c6 · outbound

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 36

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Observation c790ca46-1f74-44d8-b334-edffe4d8ad79 · outbound

This paper cites This means that global equilibrium solutions are mode sta- ble.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations This means that global equilibrium solutions are mode sta- ble

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.170152Z

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Observation 0981fd09-5bcb-4d8f-8598-02343ef45a4b · outbound

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 38

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:43.799306Z

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Observation e518478b-724a-4220-849a-6ddc0889d6fa · outbound

This paper cites Taylor,Partial Differential Equations III: Nonlinear Equations , 2nd ed., Applied Mathematical Sciences, V ol.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Taylor,Partial Differential Equations III: Nonlinear Equations , 2nd ed., Applied Mathematical Sciences, V ol

Reference 40

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Observation fbb1b659-0dad-4f01-aaaf-573a6a5e71af · outbound

This paper cites Sombras, lentes y ondas gravitatorias generadas por objetos compactos as- trof´ ısicos.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Sombras, lentes y ondas gravitatorias generadas por objetos compactos as- trof´ ısicos

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.051253Z

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Observation 59389a51-0b89-4f8b-8bc6-8b512a607430 · outbound

This paper cites Disconzi, Recent developments in mathematical aspects o f relativistic ﬂuids, Living Reviews in Relativity 27, 6 (2024).

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Disconzi, Recent developments in mathematical aspects o f relativistic ﬂuids, Living Reviews in Relativity 27, 6 (2024)

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.764519Z

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Observation 4175fb95-1d76-4fe2-9775-d12b20bd17f6 · outbound

This paper cites Hiscock and L.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Hiscock and L

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.751312Z

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Observation 18c81c33-0090-488b-95d7-77d3ec290ac5 · outbound

This paper cites Ciambelli and L.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Ciambelli and L

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.738509Z

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Observation 297fb354-c950-4e11-bfcf-152e587b51b7 · outbound

This paper cites (56) The derivatives of uµ that appear in k[µν] can be replaced by B[µν] using the constraint ﬁeld C(B) µν.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations (56) The derivatives of uµ that appear in k[µν] can be replaced by B[µν] using the constraint ﬁeld C(B) µν

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.148982Z

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:43.726574Z

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Observation 99053ac1-988e-470e-81fd-4aa639e5dbcf · outbound

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 47

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Observation f7c1284e-85c7-4614-b6a5-2f86793fa532 · outbound

This paper cites Gabarrete, A.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Gabarrete, A

Reference 48

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Observation a42c96b4-38ed-4c1e-9db0-9857de3f6c48 · outbound

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 49

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Observation a325ebcb-13cf-4b81-b32c-13a2ff371c25 · outbound

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Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:43.679386Z

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Observation 71f37617-c292-4aa1-b80f-49b8a5684646 · outbound

This paper cites Sarbach and M.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Sarbach and M

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.666447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2752bdf-b03e-4a8f-8a62-379f8aeb0480 · outbound

This paper cites Abalos, On constraint preservation and strong hyperboli city, Class.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Abalos, On constraint preservation and strong hyperboli city, Class

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.605026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 49a94e8d-d84b-48f2-83e6-50b3220a1868 · outbound

This paper cites Using the com- mutator identity ( C5) in App.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Using the com- mutator identity ( C5) in App

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.085179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0cdba765-26b6-453f-b5ba-ff53ffe6f83f · outbound

This paper cites Reula, Strongly hyperbolic systems in general relativit y, Diff.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Reula, Strongly hyperbolic systems in general relativit y, Diff

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.592182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 515ff13c-f0a1-4d67-b8da-da5562b8a266 · outbound

This paper cites Eckart, The thermodynamics of irreversible pro- cesses.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Eckart, The thermodynamics of irreversible pro- cesses

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.578854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 251e9e82-88be-48de-8adc-180d62bf361d · outbound

This paper cites an unresolved cited work.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:43.565402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f1c2f3ad-24f3-4bab-90b9-ac36604c0fb3 · outbound

This paper cites Israel, Relativistic kinetic theory of a simple gas, J.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Israel, Relativistic kinetic theory of a simple gas, J

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.552773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d5293f78-6791-4df3-914b-a82c1455dc1b · outbound

This paper cites Sarbach, E.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Sarbach, E

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.523137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 442960dc-5b7e-4af0-ab99-18b660f30a3d · outbound

This paper cites Kato, Perturbation Theory for Linear Operators (Springer- V erlag, New Y ork, 1980).

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Kato, Perturbation Theory for Linear Operators (Springer- V erlag, New Y ork, 1980)

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.508786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 684d596e-358d-44a0-9c71-e75dd71a978f · outbound

This paper cites Israel and J.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Israel and J

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.494966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c719d439-a71d-4b50-aade-9f029e5d7283 · outbound

This paper cites Israel, Covariant ﬂuid mechanics and thermodynamics: An introduction, in Relativistic Fluid Dynamics , edited by A.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Israel, Covariant ﬂuid mechanics and thermodynamics: An introduction, in Relativistic Fluid Dynamics , edited by A

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:43.481194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 911e77ee-10c5-4593-8c0e-a3a405eb8580 · outbound

This paper cites Conse- quently, only derivatives of the heat ﬂux appear in this equa - tion, which simpliﬁes the principal part of the equations.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Conse- quently, only derivatives of the heat ﬂux appear in this equa - tion, which simpliﬁes the principal part of the equations

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.138898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f7621df2-ba1e-49d0-9d97-3947a66ae5d7 · outbound

This paper cites For this, one consi d- ers the principal symbol, deﬁned as A(k, U ) := Aµ(U )kµ, (73) where kµ is a given covector perpendicular to uµ.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations For this, one consi d- ers the principal symbol, deﬁned as A(k, U ) := Aµ(U )kµ, (73) where kµ is a given covector perpendicular to uµ

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.129039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d3875ce-523a-4c1f-9b55-79b3e450d1b7 · outbound

This paper cites an unresolved cited work.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 74

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:44.119054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8f87428c-b049-4760-9870-d978b7f9a5fa · outbound

This paper cites (98) Furthermore, the system is causal if 0 < β 3η ≤ 1.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations (98) Furthermore, the system is causal if 0 < β 3η ≤ 1

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:21:44.107818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4f0c5729-8d75-4d41-808d-035623f7c78d · outbound

This paper cites an unresolved cited work.

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations Unresolved cited work

Reference 122

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:21:44.074373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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