2024
DOI: 10.1002/mana.202400011
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Well‐posedness of the two‐dimensional stationary Navier–Stokes equations around a uniform flow

Mikihiro Fujii,
Hiroyuki Tsurumi

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 … Show more

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