具有温度相关输运系数的可压缩Navier-Stokes方程中稀薄波与粘性接触波组合的稳定性

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-08-26 DOI:10.1515/anona-2022-0246

W. Dong, Zhenhua Guo

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引用次数: 1

摘要

本文研究了输运系数随温度变化的一维可压缩Navier-Stokes系统的稀疏波与粘性接触波组合的大时行为。结果表明，当绝热指数γ适当地接近于1时，理想多向性气体在时间上的全局唯一解存在，并且在大的初始扰动下渐近地趋向于粘滞接触波与稀薄波的组合。新的和微妙的分析发展，以克服困难，由于小的γ - 1，以获得热核估计。此外，我们的研究结果扩展了前人的研究[F]。李黄m . j ., a . Matsumura拱门。配给。动力机械。《论文集》，第197(2010)号。89 - 116]。

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Stability of combination of rarefaction waves with viscous contact wave for compressible Navier-Stokes equations with temperature-dependent transport coefficients and large data

Abstract In this article, we study the large-time behavior of combination of the rarefaction waves with viscous contact wave for a one-dimensional compressible Navier-Stokes system whose transport coefficients depend on the temperature. It is shown that if the adiabatic exponent γ is suitably close to 1, the unique solution global in time to ideal polytropic gas exists and asymptotically tends toward the combination of a viscous contact wave with rarefaction waves under large initial perturbation. New and subtle analysis is developed to overcome difficulties due to the smallness of γ – 1 to derive heat kernel estimates. Moreover, our results extend the studies in a previous work [F. M. Huang, J. Li, and A. Matsumura, Arch. Ration. Mech. Anal. 197 (2010), no. 1, 89–116].

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.