We prove the L p-L q maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.
|ジャーナル||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|出版物ステータス||Published - 2005 11 1|
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