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

被引：0

作者：

Fujii, Mikihiro ^{[1
]}

Tsurumi, Hiroyuki ^{[2
]}

机构：

[1] Kyushu Univ, Inst Math Ind, Fukuoka 8190395, Japan

[2] Tokushima Univ, Grad Sch Technol Ind & Social Sci, Tokushima, Japan

来源：

MATHEMATISCHE NACHRICHTEN | 2024年 / 297卷 / 12期

基金：

日本学术振兴会;

关键词：

anisotropic Besov spaces; the scaling critical framework; the two-dimensional stationary Navier-Stokes equations; well-posedness; EXISTENCE; EXTERIOR;

D O I：

10.1002/mana.202400011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the solvability of the two-dimensional stationary Navier-Stokes equations on the whole plane R-2. In Fujii [Ann. PDE, 10 (2024), no. 1. Paper No. 10], it was proved that the stationary Navier-Stokes equations on R-2 is ill-posed for solutions around zero. In contrast, considering solutions around the nonzero 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.

引用

页码：4401 / 4415

页数：15

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