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

2024/07/06 by Fujii, Mikihiro, Tsurumi, Hiroyuki
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi: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 ℝ². In [6], it was proved that the stationary Navier--Stokes equations on ℝ² 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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