Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations

Fuente: arXiv
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Autori principali: Shi, Jiajin, Wang, Yi
Natura: Preprint
Pubblicazione: 2025
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author Shi, Jiajin
Wang, Yi
author_facet Shi, Jiajin
Wang, Yi
contents We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic perturbations, in particular, without zero-mass conditions. It is shown that if the composite wave strength and the initial perturbations are suitably small, then 3D Navier-Stokes system admits a unique global-in-time strong solution which time-asymptotically converges to the corresponding composite wave up to a time-dependent shift for planar viscous shock. Our proof is based on the $a$-contraction method with time-dependent shift and suitable weight function.
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id arxiv_https___arxiv_org_abs_2502_09321
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations
Shi, Jiajin
Wang, Yi
Analysis of PDEs
We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic perturbations, in particular, without zero-mass conditions. It is shown that if the composite wave strength and the initial perturbations are suitably small, then 3D Navier-Stokes system admits a unique global-in-time strong solution which time-asymptotically converges to the corresponding composite wave up to a time-dependent shift for planar viscous shock. Our proof is based on the $a$-contraction method with time-dependent shift and suitable weight function.
title Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations
topic Analysis of PDEs
url https://arxiv.org/abs/2502.09321