Large-time behavior of composite waves of viscous shocks for the barotropic Navier-Stokes equations

2022/07/13 by Sung-Ho Han, Moon-Jin Kang, Han, Sungho +3 · 4 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Geophysics and Gravity Measurements #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2207.05989

openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the large-time behavior of the 1D barotropic Navier-Stokes flow perturbed from Riemann data generating a composition of two shock waves with small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, towards a composition of two viscous shock waves as time goes to infinity, up to dynamical shifts. Especially, the strengths of the two waves can be chosen independently. This is the first result for the convergence to a composite wave of two viscous shocks with independently small amplitudes.

Cited by

• Asymptotic stability of planar viscous shock wave to three-dimensional relaxed compressible Navier-Stokes equations
• Stability of viscous shock for the Navier-Stokes-Fourier system: outflow and impermeable wall problems
• Asymptotic stability of composite waves of shock profile and rarefaction for the Navier-Stokes-Poisson system
• Traveling Wave Solutions to a Large Class of Brenner-Navier-Stokes-Fourier Systems

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