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arXiv · 2208.01458

Asymptotic properties of steady plane solutions of the Navier-Stokes equations in the exterior of a half-space

Lili Wang·Wendong Wang
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Abstract

Motivated by Gilbarg-Weinberger's early work on asymptotic properties of steady plane solutions of the Navier-Stokes equations on a neighborhood of infinity \cite{GW1978} , we investigate asymptotic properties of steady plane solutions of this system on a half-neighborhood of infinity with finite Dirichlet integral and Navier-slip boundary condition, and obtain that the velocity of the solution grows more slowly than $\sqrt{\log r}$, while the pressure converges to $0$ along each ray passing through the origin.

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Lili Wang, Wendong Wang. 2022-08-02. Asymptotic properties of steady plane solutions of the Navier-Stokes equations in the exterior of a half-space. https://arxiv.org/abs/2208.01458

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