Global classical solutions to the 1-D vacuum free boundary problem for full compressible Navier-Stokes equations with large data

被引:4
|
作者
Ou, Yaobin [1 ]
机构
[1] Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China
关键词
DENSITY-DEPENDENT VISCOSITY; NONLINEAR ASYMPTOTIC STABILITY; LANE-EMDEN SOLUTIONS; GASEOUS STAR PROBLEM; EULER EQUATIONS; PHYSICAL VACUUM; WELL-POSEDNESS; INTERFACE BEHAVIOR; SELF-GRAVITATION; SMOOTH SOLUTIONS;
D O I
10.1063/1.4974051
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The vacuum free boundary problem of one-dimensional non-isentropic compressible Navier-Stokes equations with large initial data is investigated in this paper. The fluid is initially assumed to occupy a finite interval and connect to the vacuum continuously at the free boundary, which is often considered in the gas-vacuum interface problem. Using the method of Lagrangian particle path, we derive some point-wise estimates and weighted spatial and time energy estimates for the classical solutions. Then the global existence and uniqueness of classical solutions are shown, and the expanding speed for the free boundary is proved to be finite. The main difficulty of this problem is the degeneracy of the system near the free boundary. Previous results are only for the solutions with low regularity (cf. [G.Q. Chen and M. Kratka, Commun. Partial Differ. Equations. 27 907-943 (2002)]). Published by AIP Publishing.
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页数:21
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