Global strong solutions to 1-D vacuum free boundary problem for compressible Navier Stokes equations with variable viscosity and thermal conductivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:474

Article

Li, Zilai^1,2  Ma, Yan³  Ou, Yaobin³ 

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China

[3] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

关键词: Full Navier-Stokes equations;    Variable viscosity and thermal conductivity;    Free boundary;    Global strong solution;   

DOI  :  10.1016/j.jmaa.2019.02.009

来源: Elsevier

【 摘 要 】

In this paper, we investigate the vacuum free boundary problem of one-dimensional heat-conducting compressible Navier-Stokes equations where the viscosity coefficient depends on the density, and the heat conductivity coefficient depends on the temperature, satisfying a physical assumption from the Chapman-Enskog expansion of the Boltzmann equation. The fluid connects to the vacuum continuously, thus the system is degenerate near the free boundary. The global existence and uniqueness of strong solutions for the free boundary problem are established when the initial data are large. The result is proved by using both the Lagrangian mass coordinate and the Lagrangian trajectory coordinate. An key observation is that the Jacobian between these coordinates are bounded from above and below by positive constants. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free