Speaker
Senjo Shimizu
(Kyoto University)
Description
A time-dependent free surface problem for the Navier-Stokes equations which describes the motion of viscous fluid in a domain close to the half-space is considered. We discuss well-posedness of the problem for an initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space. Utilizing the almost orthogonal properties between the boundary potential and the Littlewood-Paley decomposition, we show maximal $L^1$-regularity in the Besov and the Lizorkin-Triebel spaces. This is a joint work with Takayoshi Ogawa (Waseda University).
Author
Senjo Shimizu
(Kyoto University)