Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations

2024/03/23 by Peng, Yi, Shi, Xiaoding, Wu, Yuhang
#35B40 #35B65 #35C20 #35M10 #35Q35 #76N10 #76T30 #Analysis of PDEs (math.AP) #FOS: Mathematics #G.1.8

paper · doi:10.48550/arxiv.2403.15663

Abstract

In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to H¹(ℝ), L²(ℝ)∩ L⁴(ℝ) and L²(ℝ), provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to L²(ℝ) can be arbitrarily large.

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