Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane

Fujii, Mikihiro

doi:10.1007/s40818-024-00174-z

Ann. PDE

2024

DOI: 10.1007/s40818-024-00174-z

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Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane

Mikihiro Fujii

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

Fujii,

Tsurumi

2024

Mathematische Nachrichten

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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.

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

Fujii,

Tsurumi

2024

Mathematische Nachrichten

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Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane

Cited by 1 publication

References 29 publications

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

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

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