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

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  • Mikihiro Fujii
  • Hiroyuki Tsurumi

Abstract

In this paper, we consider the solvability of the two‐dimensional stationary Navier–Stokes equations on the whole plane R2$\mathbb {R}^2$. In Fujii [Ann. PDE, 10 (2024), no. 1. Paper No. 10], it was proved that the stationary Navier–Stokes equations on R2$\mathbb {R}^2$ 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.

Suggested Citation

  • Mikihiro Fujii & Hiroyuki Tsurumi, 2024. "Well‐posedness of the two‐dimensional stationary Navier–Stokes equations around a uniform flow," Mathematische Nachrichten, Wiley Blackwell, vol. 297(12), pages 4401-4415, December.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:12:p:4401-4415
    DOI: 10.1002/mana.202400011
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