纳维-斯托克斯方程的旋涡勒雷- $$\alpha $$ 模型，粘度取决于到墙壁的距离

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-05-07 DOI:10.1007/s00033-024-02252-5

Guillaume Leloup

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引用次数: 0

摘要

我们引入了一个涡度Leray-(α)模型，它的涡粘度取决于(d(x,\partial \Omega )^\eta)，其中$\partial \Omega $是域的边界，$\eta \in ]0;1[$。我们证明，当（α）变为 0 时，这个系统有相当规则的弱解收敛于参考系统的解

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Vorticity Leray- $$\alpha $$ model for Navier–Stokes equations with viscosity depending on the distance to the wall

We introduce a vorticity Leray-$\alpha $ model with eddy viscosity depending on $d(x,\partial \Omega )^\eta $ where $\partial \Omega $ is the boundary of the domain and $\eta \in ]0;1[$. We prove that this system admits fairly regular weak solutions converging when $\alpha $ goes to 0 to the solution of a reference system

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Zeitschrift für angewandte Mathematik und Physik

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