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arXiv · 2409.16166

Euler equations with non-homogeneous Navier slip boundary condition

N. V. Chemetov·S. N. Antontsev
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Abstract

We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions can be written in the form $\mathbf{v}\cdot \mathsf{n}=a,$ $2D(\mathbf{v})\mathsf{n}\cdot \mathsf{s}+\alpha \mathbf{v}% \cdot {\mathsf{s}}=b,$ where the tensor $D(\mathbf{v})$ is the rate-of-strain of the fluid's velocity $\mathbf{v}$ and\ $\mathsf{(n},% \mathsf{s)}$ is the pair formed by the normal and tangent vectors to the boundary. We establish the solvability of this problem in the class of solutions with $L_{p}-$bounded \ vorticity, $p\in (2,\infty ].$ To prove the solvability we realize the passage to the limit in Navier-Stokes equations with vanishing viscosity.

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N. V. Chemetov, S. N. Antontsev. 2024-09-24. Euler equations with non-homogeneous Navier slip boundary condition. https://arxiv.org/abs/2409.16166

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