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From Navier-Stokes to BV solutions of the barotropic Euler equations

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arxiv 2401.09305 v3 pith:VICZSXCM submitted 2024-01-17 math.AP

Geng Chen , Moon-Jin Kang , Alexis F. Vasseur This is my paper · ORCID
classification math.AP
keywords solutionsequationsnavier-stokeseulerinviscidlimitsbarotropiccompressible
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abstract

In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of solving this intricate problem, particularly concerning singular solutions, persists in both compressible and incompressible scenarios. This article focuses on small $BV$ solutions to the barotropic Euler equation in one spatial dimension. Our investigation demonstrates that these solutions are inviscid limits for solutions to the associated compressible Navier-Stokes equation. Moreover, we extend our findings by establishing the well-posedness of such solutions within the broader class of inviscid limits of Navier-Stokes equations with locally bounded energy initial values.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Vanishing viscosity limit to two interacting shocks from the same family for the compressible Navier-Stokes equations

    math.AP 2026-08 conditional novelty 7.0 of 10

    For small viscosity and small wave strengths, the authors construct global smooth Navier-Stokes solutions that converge with explicit rates to the entropy solution of the Euler equations through two interacting same-f...

  2. Vanishing viscosity limit for $n\times n$ hyperbolic system of conservation laws in 1-d with nonlinear viscosity: Part-I Uniform BV estimates

    math.AP 2025-12 conditional novelty 7.0 of 10

    Small-BV data for u_t + A(u)u_x = ε(B(u)u_x)_x with commuting A, B yield a uniform-in-ε total-variation bound, and the conservative case has a unique Liu-admissible vanishing-viscosity limit.

  3. Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows

    math.AP 2025-05 conditional novelty 6.0 of 10

    Small isothermal Euler shocks are stable and unique in the class of vanishing viscosity limits, even under large perturbations of finite relative entropy.

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