%0 Journal Article
%T 三维粘性系数依赖于密度的不可压缩热传导Navier-Stokes方程的全局强解<br>Global Strong Solution for 3D Viscous Incompressible Heat Conducting Navier-Stokes Equations with Density-Dependent Viscosity
%A 王智辉
%J Advances in Applied Mathematics
%P 826-842
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.144210
%X 本文研究了三维粘性系数依赖于密度的非齐次不可压缩热传导Navier-Stokes方程。首先&#65292;当粘性系数的梯度的范数满足<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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时&#65292;存在一个整体强解&#65292;此外&#65292;如果初始能量适当小&#65292;证明了三维粘性非齐次热传导变粘性Navier-Stokes方程整体强解的唯一性。<br>In this paper, we investigate an 3D viscosity incompressible heat conducting Navier-Stokes equations with density-dependent viscosity. First, we obtain that there exists a global strong solution provided the norm of the gradient of viscosity satisfies <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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. Moreover, if energy is suitably small, we show the uniqueness of the global strong solution to the three-dimensional viscous non-homogeneous heat conducting Navier-Stokes equations with variable viscosity.
%K 全局强解&#65292
%K 热传导Navier-Stokes方程&#65292
%K 粘性相关密度&#65292
%K 不可压缩<br>Global Strong Solution
%K Heat Conducting Navier-Stokes Equations
%K Density-Dependent Viscosity
%K Incompressible
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113019