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arXiv · 2407.05012

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

Mikihiro Fujii·Hiroyuki Tsurumi
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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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Mikihiro Fujii, Hiroyuki Tsurumi. 2024-07-06. Well-posedness of the two-dimensional stationary Navier--Stokes equations around a uniform flow. https://arxiv.org/abs/2407.05012

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