On the Ladyzhenskayaï-½Smagorinsky turbulence model of the Navierï-½Stokes equations in smooth domains. The regularity problem
On the Ladyzhenskayaï-½Smagorinsky turbulence model of the Navierï-½Stokes equations in smooth domains. The regularity problem
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光滑域中 Navierï-½Stokes 方程的 Ladyzhenskayaï-½Smagorinsky 湍流模型 正则性问题。
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发表时间：
2009
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通讯作者：
H. B. Veiga
中科院分区：
文献类型：
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作者：
H. B. Veiga
我们建立正则性结果的边界的解决方案，广义斯托克斯和Navier-Stokes方程系统的固定和发展的情况下。这里一般化的意思是存在剪切依赖性粘度。我们在这里处理的情况下$pgeq 2 $。实际上，我们感兴趣的是证明正则性结果在$L ^q（Ω）$空间的所有二阶导数的速度和所有的一阶导数的压力。本文的主要目的是将我们以前在文献cite {bvlali}和cite {bvcubo}中介绍的平边界情形的格式推广到曲线边界的情形。
We establish regularity results up to the boundary for solutions to generalized Stokes and Navier-Stokes systems of equations in the stationary and in the evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat here the case $pgeq 2$. Actually, we are interested in proving regularity results in $L^q(Omega)$ spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced in references cite{bvlali} and cite{bvcubo} for the flat-boundary case, to the case of curvilinear boundaries.