Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow

Mikihiro Fujii, Hiroyuki Tsurumi

Type: Preprint

Publication Date: 2024-07-06

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2407.05012

Abstract

In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $\mathbb{R}^2$. In [6], it was proved that the stationary Navier--Stokes equations on $\mathbb{R}^2$ is ill-posed for solutions around zero. In contrast, considering solutions around the non-zero constant flow, the perturbed system has a better regularity in the linear part, which enables us to prove the unique existence of solutions in the scaling critical spaces of the Besov type.

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arXiv (Cornell University) - View - PDF

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