LOCAL CLASSICAL SOLUTIONS TO THE FULL COMPRESSIBLE NAVIER-STOKES SYSTEM WITH TEMPERATURE-DEPENDENT HEAT CONDUCTIVITY

被引：0

作者：

Cao, Yue ^{[1
]}

Li, Yachun ^{[2
,3
]}

Zhu, Shengguo ^{[3
,4
,5
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, CMA Shanghai, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

[4] Shanghai Jiao Tong Univ, CMA Shanghai, Sch Math Sci, Shanghai 200240, Peoples R China

[5] Univ Oxford, Math Inst, Oxford OX2 6GG, England

来源：

METHODS AND APPLICATIONS OF ANALYSIS | 2021年 / 28卷 / 02期

关键词：

Full compressible Navier-Stokes system; three dimensions; classical solutions; vacuum; temperature-dependent heat conductivity; VISCOUS POLYTROPIC FLUIDS; BOUNDARY-VALUE-PROBLEMS; DEGENERATE VISCOSITIES; WELL-POSEDNESS; CAUCHY-PROBLEM; EQUATIONS; VACUUM; EXISTENCE; TIME; GAS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the full compressible Navier-Stokes equations in a bounded domain Omega subset of R-3, where the heat conductivity depends on the temperature theta in a power law (theta(b) for some constant b > 0) of Chapman-Enskog. We first prove the existence of the unique strong solution with non-negative mass density and arbitrarily large data, and then lift the regularities to get a classical one. The corresponding proof is nontrivial due to the appearance of the vacuum and the strong nonlinearity of the temperature-dependent heat conductivity. We introduce a new variable theta(b)(+1) to reformulate and simplify the system, and require that the measure of the initial vacuum domain is sufficiently small, for example, the initial vacuum only appears in some one-dimensional curves or two-dimensional surfaces.

引用

页码：105 / 152

页数：48

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