Stability of the planar rarefaction wave to two-dimensional compressible Navier-Stokes equations

2017/10/17 by Linan Li, Yi Wang, Li, Lin-an +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1710.06063

openalex publication_date 2017/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well-known that the rarefaction wave, one of the basic wave patterns to the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional compressible Navier-Stokes equations (cf. [14,15,12,17]). In the present paper we proved the time-asymptotically nonlinear stability of the planar rarefaction wave to the two-dimensional compressible and isentropic Navier-Stokes equations, which gives the first stability result of the planar rarefaction wave to the multi-dimensional system with physical viscosities.

Citations

• Hyperbolic systems of conservation laws II
• On contact discontinuities in multi-dimensional isentropic Euler equations

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