On the Stokes equations with the Navier-type boundary conditions

Cherif Amrouche; Nour El Houda Seloula

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On the Stokes equations with the Navier-type boundary conditions

机译：具有Navier型边界条件的Stokes方程

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In a possibly multiply-connected three dimensional bounded domain, we prove in the L p theory the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying non homogeneous boundary conditions. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u · n = g and curl u× n = h× n on the boundary Γ . We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are mainly based on Inf . Su p conditions.

机译：在一个可能多重连接的三维有界域中，我们在L p理论中证明了矢量势的存在和唯一性，它与无散度函数相关并且满足非齐次边界条件。此外，我们考虑具有非标准边界条件的平稳Stokes方程，其边界形式为u·n = g，并且在边界Γ上卷曲u×n = h×n。我们证明了弱，强和非常弱的解决方案的存在和唯一性。我们的证明主要基于Inf。条件。

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《Differential Equations Applications》 |2011年第4期|共27页
作者
Cherif Amrouche; Nour El Houda Seloula;
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中图分类微分方程、积分方程;
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3. ON A v-CONTINUOUS FAMILY OF STRONG SOLUTIONS TO THE EULER OR NAVIER-STOKES EQUATIONS WITH THE NAVIER-TYPE BOUNDARY CONDITION [J] . Hamid Bellout, Jiri Neustupa, Patrick Penel Discrete and continuous dynamical systems . 2010,第4期

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6. A semi-implicit augmented IIM for Navier–Stokes equations with open traction or free boundary conditions [O] . Zhilin Li, Li Xiao, Qin Cai, -1

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7. Stokes and Navier-Stokes problems with Navier-type boundary condition in L^p-spaces [O] . Hind Al Baba, Cherif Amrouche 2019

机译：Stokes和Navier-Stokes在L ^ p空间中的Navier型边界条件存在问题

On the Stokes equations with the Navier-type boundary conditions

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