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On the maximal Lp- Lq theory arising in the study of a free boundary problem for the Navier-Stokes equations

By Yoshihiro Shibata

Department of Mathematics and Research Institute of Science and Engineering, Waseda University, Japan

Fluid Mechanics

Published: Sep 17, 2018 | pg. no: 1-69

Abstract: Solonnikov introduced a new system of the linear equations to treat the nonlinear problem obtained by the so called Hanzawa coordinate transformation to the free boundry problem for the Navier-Stokes equations in order to write it in a fixed domain. And, he proved the maximal regularity theorem in the L2 Sobolev-Slobodetskii space in a bounded domain. In this paper, we prove the maximal Lp-Lq regu ...[Read more]

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