The vorticity equations in a half plane with measures as initial data

Abe, Ken

doi:10.1016/j.anihpc.2020.10.002

Abe, Ken ¹

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.

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Résumé

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 $L^{1}$ -estimate of a solution operator for the vorticity equations associated with the Stokes equations.

Reçu le : 2019-10-12
Révisé le : 2020-09-24
Accepté le : 2020-10-20

DOI : 10.1016/j.anihpc.2020.10.002

Classification : 35Q35, 35K90
Mots-clés : Vorticity equations, Half plane, Finite measures

Affiliations des auteurs :

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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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. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.10.002/

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