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Recent developments in mathematical aspects of relativistic fluids
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We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs' main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
Forward citations
Cited by 6 Pith papers
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The Lorentzian geometry of relaxation
Causality forces purely relaxational dispersion relations to follow spacelike trajectories on the Lorentzian {iω,ik} plane, producing universal bounds on diffusivity, viscosity, time-dilation deviations, and hydrodyna...
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Nonlinear Causality and Strong Hyperbolicity of Einstein-Israel-Stewart Theories of Transient Relativistic Fluid Dynamics
Necessary and sufficient algebraic inequalities fully characterize nonlinear causality of general Israel-Stewart bulk-plus-shear theories, with sufficient conditions for strong hyperbolicity and constraint propagation...
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Extending Israel-Stewart theory: Causal bulk viscosity at large gradients
A new family of polytropic bulk-viscous fluids reduces to Israel-Stewart near equilibrium and stays causal, symmetric hyperbolic, and thermodynamically consistent for arbitrarily large viscous stresses.
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Effective action for relativistic hydrodynamics from Crooks fluctuation theorem
A new path-integral framework for relativistic fluctuating hydrodynamics uses a covariant Crooks fluctuation theorem to impose KMS symmetry and derive fluctuation-dissipation relations, with criteria for causality and...
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Gaussian non relativistic spontaneously stochastic hydrodynamics
The paper proposes that non-relativistic incompressible hydrodynamics is the infrared limit of a Gaussian stochastic theory, with compressible-scale counterterms generating spontaneous stochasticity and anomalous dissipation.
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Causality of polarizeable dissipative fluids from Lagrangian hydrodynamics
In a Lagrangian model of polarized dissipative fluids, causality couples the spin, shear, and bulk relaxation times through inequalities that can make polarization mask viscosity.
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