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

Abstract

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.