Geodesic
The vorticity equations in a half plane with measures as initial data
Abe, Ken1
1 Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku Osaka, 558-8585, Japan
Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1055-1094 Cet article a éte moissonné depuis la source Numdam

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We consider the two-dimensional Navier-Stokes equations subject to the Dirichlet boundary condition in a half plane for initial vorticity with finite measures. We study local well-posedness of the associated vorticity equations for measures with a small pure point part and global well-posedness for measures with a small total variation. Our construction is based on an L1-estimate of a solution operator for the vorticity equations associated with the Stokes equations.

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DOI : 10.1016/j.anihpc.2020.10.002
Classification : 35Q35, 35K90
Keywords: Vorticity equations, Half plane, Finite measures

Abe, Ken 1

1 Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku Osaka, 558-8585, Japan 
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     title = {The vorticity equations in a half plane with measures as initial data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Abe, Ken. The vorticity equations in a half plane with measures as initial data. Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1055-1094. doi: 10.1016/j.anihpc.2020.10.002

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