{"id":"f551e9da-68b3-4cca-b5eb-379a310b3584","arxiv_id":"1908.06228","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The 2D stochastic Navier-Stokes equations with multiplicative Levy noise have unique strong solutions and satisfy a Freidlin-Wentzell large deviation principle under square-integrable Lipschitz and growth assumptions.","lead":"This paper proves that the 2D stochastic Navier-Stokes equations driven by jump noise have unique strong solutions under mild Lipschitz and growth conditions, and it derives a large deviation principle for these solutions. The value is that the result covers multiplicative Levy noise with only square-integrable coefficients, a setting where earlier work needed extra assumptions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Assumption 3.1's exponential integrability is only local; the uniform estimate (B.2) used to prove the LDP needs global exponential integrability, so the central claim is not established as stated.","rationale":"The reader correctly identified the exponential-integrability condition in Assumption 3.1 as the load-bearing assumption for the LDP, and I agree that the abstract's wording overclaims. However, the more serious issue is that the condition as written is local, whereas the uniform control (B.2) and (3.25) used throughout the LDP proof needs a global exponential moment. The paper's definition of H, with integrability over every ν-finite Γ, does not imply global integrability when ν is σ-finite but infinite, and I constructed an explicit L∈H∩L^2(ν) and g∈S_N for which ∫ L|g-1|ν is infinite. This invalidates the proof of Lemma 3.1, Proposition 3.3, and the applicability of the weak-convergence theorem from [19]. I still believe the intended theorem is likely correct under the standard global exponential-integrability hypothesis used in [19], so the appropriate verdict is conditional acceptance with a required strengthening of Assumption 3.1, rather than outright rejection. Credit is due for the detailed well-posedness proofs and the self-contained Girsanov argument, but the central LDP claim is not supported by the hypotheses as written.","tokens_in":63477,"tokens_out":19565,"duration_ms":211171,"concrete_test":"One decisive check is to test (B.2) against the counterexample above. Fix Z=N, ν({n})=n^{-2}, L(n)=n^{1/4}; then L satisfies the local condition H and L∈L^2(ν). Let n_k=2^k and define g∈S_N by g(t,n_k)=2^{7k/4} on [0,T] and g(t,z)=1 otherwise. Compute: relative entropy R(g)=T∑_k [g log g -g+1]ν({n_k}) ≈ T∑_k k 2^{-k/4}<∞, so g∈S_N, while the integral in (B.2) is ∫_0^T∫_Z L|g-1|ν dz dt ≥ T∑_k 2^{k/4}2^{7k/4}2^{-2k}=∞. If the authors maintain that (B.2) holds under Assumption 3.1, this computation must fail somewhere; identify the step. If it cannot, then Assumption 3.1 must be replaced by the global exponential integrability condition used in [19], and all subsequent estimates re-verified under that stronger hypothesis.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The proof of Theorem 3.1 rests on the uniform estimate (B.2) and its variant (3.25), obtained by invoking Lemma 3.4 of [19]. That lemma requires global exponential integrability, e.g. ∫_Z exp(θρ(z)^2)ν(dz)<∞ for some θ>0. Assumption 3.1 only requires L_i∈H, i.e. ∫_Γ exp(δL_i^2)dν<∞ for every ν-finite Γ; under σ-finite ν this is strictly local and does not imply the global condition. This is not a pedantic distinction: local H∩L^2(ν) does not imply (B.2). Concrete failure: take Z=N, ν({n})=n^{-2}, L(n)=n^{1/4}. Then L∈L^2(ν) (∑ n^{-3/2}<∞) and L∈H (every finite Γ is trivial), but ∑_n exp(δ n^{1/2})/n^2=∞ for every δ>0. Moreover, set n_k=2^k and g(t,n_k)=2^{7k/4} on [0,T], g=1 elsewhere. The relative entropy is T∑_k [g log g -g+1]ν({n_k}) ≈ T∑_k k 2^{-k/4}<∞, so g∈S_N for a finite N, while ∫_0^T∫_Z L|g-1|ν dz dt ≥ T∑_k 2^{k/4}2^{7k/4}2^{-2k}=∞. Hence (B.2) is false under Assumption 3.1. Consequently Lemma 3.1 (existence of u^g for every g∈S_N) and Proposition 3.3 are not justified, and the weak-convergence framework of [19] cannot be applied. In fact, with G(y,z)=L(z)y and u0≠0, the right-hand side of equation (3.10) contains an infinite drift for such g, so the skeleton equation may have no finite solution. The fix is to strengthen Assumption 3.1 to global ∫_Z exp(δL_i^2)dν<∞ (or otherwise prove (B.2) under the stated hypothesis).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the 2D stochastic Navier-Stokes equations driven by multiplicative Lévy noise. It proves existence and uniqueness of global strong solutions in both the probabilistic and PDE senses under Lipschitz and linear growth assumptions on the jump coefficient (Theorems 2.1 and 2.2), proves a Girsanov-type theorem for Poisson random measures, and uses the weak-convergence framework of [19,18] to establish a Freidlin-Wentzell large deviation principle on the space Υ_V_T = D([0,T],V) ∩ L^2([0,T],D(A)) (Theorem 3.1). The rate function is defined through a deterministic skeleton equation (3.10).","tokens_in":63946,"tokens_out":5169,"duration_ms":50968,"significance":"If the main results hold, the paper would improve on prior work by treating strong solutions in the PDE sense for the 2D Navier-Stokes equations with jumps, and it would provide a rigorous and self-contained proof of the Poisson Girsanov transformation needed for the weak-convergence approach. The fixed-point constructions and the a priori estimates in Sections 2 and 4 are extensive and mostly carefully organized. However, the central LDP theorem depends on the uniform estimate (B.2), and that estimate is not justified under the stated Assumption 3.1: the local exponential integrability condition defining the class H is strictly weaker than the global exponential integrability required by Lemma 3.4 of [19]. A concrete counterexample shows that (B.2) can fail under Assumption 3.1, and in that case the skeleton equation (3.10) may not be well-posed for some g ∈ S_N. Since Lemma 3.1, Proposition 3.3, and Proposition 4.1 all rely on this estimate, Theorem 3.1 is not established as stated. The gap appears repairable by strengthening the assumption on L_i to a global exponential integrability condition.","major_comments":[{"comment":"Assumption 3.1 only requires L_i ∈ H, i.e. ∫_Γ exp(δL_i^2(z))ν(dz) < ∞ for every ν-finite set Γ. Under a σ-finite ν this is a purely local condition. The paper then invokes Lemma 3.4 of [19] to assert (B.2), namely that sup_{g∈S_N} ∫_0^T ∫_Z L_i(z)|g(t,z)-1|ν(dz)dt < ∞ for i=1,2,3. Lemma 3.4 of [19] requires a global exponential integrability condition such as ∫_Z exp(θρ(z)^2)ν(dz)<∞ for some θ>0. Local H-integrability does not imply this. For example, take Z=N, ν({n})=n^{-2}, and L(n)=n^{1/4}; then L∈L^2(ν) and L∈H, but ∑_n exp(δ n^{1/2})/n^2 = ∞ for every δ>0. Thus (B.2) cannot be derived from Assumption 3.1.","section":"Section 3.1 and Appendix B, Eq. (B.2)"},{"comment":"Because (B.2) is used at the start of the proof of Lemma 3.1 to ensure that the drift F(t,y)=∫_Z G(y,z)(g(t,z)-1)ν(dz) is integrable and locally Lipschitz, the claimed well-posedness of the skeleton equation for every g∈S_N is not established under Assumption 3.1. The failure is not merely technical: with G(y,z)=L(z)y, u0≠0, and the function g constructed in the previous counterexample (g(t,n_k)=2^{7k/4} on n_k=2^k and g=1 elsewhere), one has g∈S_N but ∫_0^T∫_Z L(z)|g(t,z)-1|ν(dz)dt=∞, so the right-hand side of (3.10) is infinite and no finite solution can exist. Lemma 3.1 should either be proved under the stated hypothesis or Assumption 3.1 should be strengthened to a global exponential integrability condition for L_i.","section":"Lemma 3.1 / equation (3.10)"},{"comment":"Proposition 3.3, which verifies Claim-LDP-1, uses (B.2) at several essential points: in the estimates (3.24), (3.26), (3.28), and (3.32), and in the final Gronwall step. Lemma 4.4 and Lemma 4.5 similarly use (B.2) to control the stochastic and drift terms of the controlled equation (4.34). Therefore Claim-LDP-2 is also not justified as written. The whole weak-convergence argument for Theorem 3.1 collapses unless (B.2) is replaced by a valid estimate; a global exponential integrability assumption on L_i would restore it.","section":"Propositions 3.3 and 4.1"}],"minor_comments":[{"comment":"The abstract says the paper works under 'local Lipschitz and one-sided linear growth assumptions', but Theorems 2.1 and 2.2 are stated under global Lipschitz and linear growth conditions, namely (G-H1), (G-H2) and (G-V1), (G-V2). The wording should be aligned with the actual assumptions.","section":"Abstract and Section 2"},{"comment":"In the Itô estimate for the proof of Theorem 2.2, the decomposition writes a sum over five terms J_i(t), but only J_2 through J_5 are defined; J_1 appears to be the initial condition term. Please correct the indexing.","section":"Section 2.2, equation (2.94)"},{"comment":"The proof invokes [55, Theorem 8] to obtain the measurable maps G^ε. It would help the reader if the hypotheses of that theorem were checked explicitly against the present setting, since the entire weak-convergence argument depends on this measurable-selection step.","section":"Section 3.1, proof of Theorem 3.1"},{"comment":"There are several typos and small notational slips, e.g. 'uniqueness element' in the proof of Theorem 2.2, the inconsistent notation U^N versus U_N around (3.18) and Section 4.2, and the unnumbered display '5∑_{i=1}' in (2.94). A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is built heavily on the first author's previous framework and on [19] and [55]; the genuinely new contribution is the LDP for strong PDE solutions with the accompanying Girsanov theorem. The gap in Assumption 3.1 is concentrated but crucial. I believe it is repairable by strengthening the exponential integrability condition to a global one, so I would not reject outright. The authors should also verify that the corrected assumption is compatible with the examples and related literature cited in the introduction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: the paper's first half is a genuine improvement and seems solid. Theorem 2.1 and 2.2 prove global strong solutions for 2D Navier-Stokes with multiplicative Lévy noise under essentially the natural global Lipschitz and linear growth assumptions, where previous work needed extra p-th moment or small-jump conditions. The cut-off fixed point argument is long but structurally coherent, and the estimates are there. The Girsanov theorem for Poisson random measures is also proved in detail and is independently useful.\n\nThe second thing is less good. The LDP as stated is not proved. The proof of Theorem 3.1 rests on (B.2), the uniform integrability bound for ∫ L_i(z)|g-1|ν(dz) over S_N, obtained from Lemma 3.4 of [19]. Assumption 3.1 only puts L_i in H ∩ L^2(ν), and H is a local condition: for every finite ν-measure set Γ, ∫_Γ exp(δ h^2)dν < ∞. That does not imply the global estimate that Lemma 3.4 needs. The concrete counterexample in the stress-test note is correct: on Z=N with ν({n})=n^{-2}, L(n)=n^{1/4} is in L^2 and in H locally, but there are g's of finite relative entropy with ∫ L|g-1|ν = ∞. For G(y,z)=L(z)y, equation (3.10) can have infinite drift for those g, so Lemma 3.1 (existence of u^g for all g∈S_N) fails, and the weak-convergence framework of [19] cannot be applied. The fix is straightforward: strengthen Assumption 3.1 to a global exponential integrability condition ∫_Z exp(δ L_i^2)dν < ∞, or prove the uniform bound another way. But as written, Theorem 3.1 is not established.\n\nMinor: the abstract promises 'local Lipschitz and one-sided linear growth', while Assumption 2.1 is global Lipschitz and linear growth; this should be corrected.\n\nNet: the well-posedness part deserves to survive and is worth citing. The LDP part needs real revision. I would send this to a serious referee, but the referee should be asked to check the LDP assumptions carefully and to require the global exponential condition before publication.","headline":"The well-posedness half is credible and useful; the LDP half has a load-bearing gap: Assumption 3.1 is too weak for the uniform estimate (B.2), so Theorem 3.1 is not established as stated.","tokens_in":64503,"tokens_out":3288,"would_cite":true,"duration_ms":33352,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60H15","60F10","76D06","76M35"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proves that 2-D stochastic Navier–Stokes equations with multiplicative Lévy noise have unique global strong solutions under natural Lipschitz and linear-growth assumptions, and satisfy a Freidlin–Wentzell large deviation…","keywords":["2-D stochastic Navier-Stokes equations","Lévy processes","multiplicative jump noise","Poisson random measure","Girsanov theorem","Freidlin-Wentzell large deviation principle","strong solutions","weak convergence method"],"falsifier":"A concrete check: let $Z=(0,1)$, $\\nu(dz)=dz$, $L_i(z)=-\\log z$, and $G(u,z)=L_1(z)u$, so that $\\int_Z L_i^2\\,d\\nu<\\infty$ but $\\int_Z e^{\\delta L_i^2}\\,d\\nu=\\infty$ for all $\\delta>0$. For this coefficient, compute whether the family $\\{u^\\varepsilon\\}$ satisfies the large deviation principle with the rate function $I$ of Theorem 3.1: if it does, Assumption 3.1 is not necessary; if the Laplace upper or lower bound fails, the exponential-integrability condition is genuinely load-bearing.","tokens_in":63240,"feed_emoji":"🌊","tokens_out":14073,"duration_ms":121012,"temperature":0.7,"pith_summary":"The paper establishes three things for the 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noise: global strong well-posedness for both $H$-valued and $V$-valued initial data under the classical Lipschitz and linear-growth assumptions on the jump coefficient; a rigorous Girsanov theorem for Poisson random measures; and a Freidlin–Wentzell large deviation principle for the PDE-strong solutions. The large deviation statement says that as the small-noise parameter $\\varepsilon$ goes to zero, the probability that the solution stays near a given path $k$ decays exponentially, and the exponent is the infimum of the relative entropy $L_T(g)$ over controls $g$ whose deterministic controlled Navier–Stokes solution equals $k$. A reader should care because jump noise is the natural model for abrupt, unpredictable events in fluid systems, and previous well-posedness results for this setting required extra conditions on the small jumps or higher integrability of the coefficient, while previous large deviation results were for probabilistically strong solutions rather than PDE-strong solutions. The proof removes those extra assumptions by combining a cut-off of the nonlinearity with a fixed-point argument and by supplying a self-contained Girsanov argument for the Poissonian control problem.","feed_headline":"Jumpy 2D fluid: strong solutions plus a large-deviation law","feed_subtitle":"Rare fluctuations obey a relative-entropy rate; the most likely path solves a deterministic equation.","key_machinery":"The proof is carried by three interlocking pieces. First, the nonlinear term is truncated by a smooth cut-off function $\\theta_m(\\|y\\|_{\\Upsilon_t})$ and further localized with $\\varphi_\\delta$; this makes the auxiliary deterministic PDE uniformly coercive, so Picard iteration and the Banach fixed-point theorem give a unique solution for each stochastic forcing path, and the cut-off is later removed by stopping times and a priori estimates. Second, a Girsanov-type theorem for Poisson random measures, with density $M^\\varepsilon_T(\\psi)$ built from the control $\\phi$, guarantees that under an equivalent probability measure the controlled process has the same law as the original noise-driven process; Lemma 4.3 uses this to identify the controlled SPDE's solution. Third, the weak-convergence criterion reduces the large deviation principle to two claims: continuity of the deterministic map $g\\mapsto u^g$ on $S_N$, and convergence in law of controlled stochastic solutions to $G^0(\\phi)$. The exponential-integrability class $H$ for the size functions $L_i$ is what makes the estimates uniform over the relative-entropy balls $S_N$.","core_discovery":"The central claim is Theorem 3.1: under Assumption 3.1, for every $f\\in L^2([0,T];H)$ and $u_0\\in V$, the family of strong solutions $\\{u^\\varepsilon\\}_{\\varepsilon>0}$ satisfies a large deviation principle on $\\Upsilon_T^V=D([0,T],V)\\cap L^2([0,T],D(A))$ with the good rate function $I(k)=\\inf\\{L_T(g): g\\in S,\\ u^g=k\\}$, where $S$ is the union over $N$ of relative-entropy balls $S_N=\\{g:L_T(g)\\le N\\}$, $L_T(g)=\\int_0^T\\int_Z(g\\log g-g+1)\\,d\\nu\\,dt$, and $u^g$ is the unique solution of the deterministic controlled equation $\\frac{d}{dt}u^g+Au^g+B(u^g)=f+\\int_Z G(u^g,z)(g-1)\\,\\nu(dz)$, $u^g(0)=u_0$. Along the way the paper proves Theorems 2.1 and 2.2: global unique solutions in $D([0,\\infty),H)\\cap L^2_{\\rm loc}([0,\\infty),V)$ and in $D([0,\\infty),V)\\cap L^2_{\\rm loc}([0,\\infty),D(A))$ under only the Lipschitz and linear-growth conditions on the jump coefficient. The paper also states and proves a Girsanov-type theorem for Poisson random measures, which is the step that converts the control problem into the original noise law.","pith_inferences":["An untested consequence is that the same cut-off and fixed-point mechanism, together with the Poisson Girsanov density, should remove the extra integrability assumptions in other dissipative SPDEs driven by Lévy noise, for example quasi-geostrophic or Landau–Lifshitz equations.","The gap between square-integrability for well-posedness and exponential integrability for the LDP suggests a boundary regime: a jump coefficient like $G(u,z)=(-\\log z)u$ on $Z=(0,1)$ with $\\nu(dz)=dz$ satisfies the well-posedness assumptions but not Assumption 3.1, and it is an open question whether the LDP still holds, perhaps with different scaling.","The rate function indicates a concrete importance-sampling scheme: replace the intensity $\\nu(dz)dt$ by the tilted intensity $g(t,z)\\nu(dz)dt$ with $g$ minimizing $L_T$; this could be tested numerically on a discretized 2D Navier–Stokes model to estimate rare-event probabilities.","Because the LDP holds in the joint space $D([0,T],V)\\cap L^2([0,T],D(A))$, it should imply Laplace principles for continuous functionals of the solution such as enstrophy or dissipation, which is a stronger statement than an LDP in weaker path topologies."],"forward_implications":["Under Assumption 3.1, the laws of $u^\\varepsilon$ satisfy a large deviation principle on $\\Upsilon_T^V$, so rare excursions from the deterministic Navier–Stokes flow are exponentially rare with a computable rate $I$.","The rate function is good: its sublevel sets are compact, and $I(k)=\\infty$ when no admissible control drives the deterministic equation to $k$.","The zero-noise most likely path is the solution of the controlled equation (3.10) with the control $g$ minimizing $L_T(g)$.","The well-posedness theorems hold under only Lipschitz and linear growth of the jump coefficient; extra small-jump control and higher-moment assumptions are not needed for existence and uniqueness of global strong solutions.","The Girsanov theorem for Poisson random measures proved in Lemma 4.2 is a reusable rigorous step for weak-convergence proofs of large deviations for SPDEs driven by jumps."],"supporting_citations":[{"why":"supplies the weak-convergence criterion for Poisson random measures and the compactness/continuity lemmas for relative-entropy balls $S_N$.","marker":"[19]"},{"why":"introduces the Poisson random measure framework and variational representation on which Section 3's control formulation rests.","marker":"[18]"},{"why":"provides the measurable-selection theorem that yields the map $\\mathcal G^\\varepsilon$ from the Poisson random measure to the strong solution.","marker":"[55]"},{"why":"supplies the Itô formula and Burkholder–Davis–Gundy estimates for jump-driven 2-D Navier–Stokes equations used throughout Sections 2 and 4.","marker":"[12]"},{"why":"supplies the local-monotone-coefficient framework for SPDEs with Lévy noise, used for uniqueness in Theorem 2.1.","marker":"[13]"},{"why":"gives the earlier PDE-strong well-posedness result under stronger assumptions that this paper improves on.","marker":"[7]"},{"why":"is the previous well-posedness result whose extra small-jump control condition the paper removes.","marker":"[24]"},{"why":"is the earlier large-deviation result for the same equation in probabilistically strong solutions, whose estimates the paper adapts for PDE-strong solutions.","marker":"[56]"},{"why":"provides the Girsanov transformation for Poisson random measures that Lemma 4.2 builds on.","marker":"[37]"},{"why":"provides the Burkholder–Davis–Gundy inequality used in the a priori estimates.","marker":"[38]"}],"fun_headline_variants":["2D Navier-Stokes with jumps: strong solutions and large deviations","Jumpy 2D fluids: global strong solutions and rare-event law","Large deviations for jumpy 2D Navier-Stokes: full well-posedness","2D stochastic Navier-Stokes with Levy noise: LDP and strong solutions","Jump-driven 2D fluids obey a large-deviation principle"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing extra premise for the large deviation theorem, beyond well-posedness, is that the jump coefficient's size functions belong to the class $H$, meaning $\\int_\\Gamma \\exp(\\delta L_i(z)^2)\\,\\nu(dz)<\\infty$ for every finite-measure set $\\Gamma$, since only square-integrability is enough for the well-posedness theorems but not for the uniform estimates over the relative-entropy balls.","fun_headline_variants_meta":{"raw":{"variants":["2D Navier-Stokes with jumps: strong solutions and large deviations","Jumpy 2D fluids: global strong solutions and rare-event law","Large deviations for jumpy 2D Navier-Stokes: full well-posedness","2D stochastic Navier-Stokes with Levy noise: LDP and strong solutions","Jump-driven 2D fluids obey a large-deviation principle"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000835,"raw_usage":{"total_tokens":3688,"prompt_tokens":1032,"completion_tokens":2656,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":648,"completion_tokens_details":{"reasoning_tokens":2556}},"tokens_in":648,"tokens_out":2656,"duration_ms":19174,"temperature":1.0,"reasoning_tokens":2556,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:53:47.207456+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete check: let $Z=(0,1)$, $\\nu(dz)=dz$, $L_i(z)=-\\log z$, and $G(u,z)=L_1(z)u$, so that $\\int_Z L_i^2\\,d\\nu<\\infty$ but $\\int_Z e^{\\delta L_i^2}\\,d\\nu=\\infty$ for all $\\delta>0$. For this coefficient, compute whether the family $\\{u^\\varepsilon\\}$ satisfies the large deviation principle with the rate function $I$ of Theorem 3.1: if it does, Assumption 3.1 is not necessary; if the Laplace upper or lower bound fails, the exponential-integrability condition is genuinely load-bearing.","supporting_citations":[{"cited_title":"Budhiraja, J","cited_arxiv_id":null,"evidence_quote":"supplies the weak-convergence criterion for Poisson random measures and the compactness/continuity lemmas for relative-entropy balls $S_N$."},{"cited_title":"Budhiraja, P.Dupuis and V","cited_arxiv_id":null,"evidence_quote":"introduces the Poisson random measure framework and variational representation on which Section 3's control formulation rests."},{"cited_title":"Zhao, Yamada-Watanabe theorem for stochastic evolutionequation driven by Poisson Random Measure, ISRN Probability and Statistics 2014 (2014) Article ID 982190, 7 pages","cited_arxiv_id":null,"evidence_quote":"provides the measurable-selection theorem that yields the map $\\mathcal G^\\varepsilon$ from the Poisson random measure to the strong solution."},{"cited_title":"Brze´ zniak, E","cited_arxiv_id":null,"evidence_quote":"supplies the Itô formula and Burkholder–Davis–Gundy estimates for jump-driven 2-D Navier–Stokes equations used throughout Sections 2 and 4."},{"cited_title":"Brze´ zniak, W","cited_arxiv_id":null,"evidence_quote":"supplies the local-monotone-coefficient framework for SPDEs with Lévy noise, used for uniqueness in Theorem 2.1."},{"cited_title":"Bessaih, E","cited_arxiv_id":null,"evidence_quote":"gives the earlier PDE-strong well-posedness result under stronger assumptions that this paper improves on."},{"cited_title":"Dong and Y","cited_arxiv_id":null,"evidence_quote":"is the previous well-posedness result whose extra small-jump control condition the paper removes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"is the earlier large-deviation result for the same equation in probabilistically strong solutions, whose estimates the paper adapts for PDE-strong solutions."},{"cited_title":"Jacod and A.N","cited_arxiv_id":null,"evidence_quote":"provides the Girsanov transformation for Poisson random measures that Lemma 4.2 builds on."},{"cited_title":"Kallenberg, Foundations of Modern Probability , Springer-Verlag, 1997","cited_arxiv_id":null,"evidence_quote":"provides the Burkholder–Davis–Gundy inequality used in the a priori estimates."}],"review_version":1}