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 . In Fujii Ann. PDE, 10 (2024), no. 1. Paper No. 10, it was proved that the stationary Navier–Stokes equations on 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.