Bio: Professor Yoshihiro Shibata obtained Doctor of Sciences under Mutsuhide Matsumura at Tukuba University in 1977. He worked in the Department of Mathematics at Tsukuba University from 1978- 97, and since 1997, he is a full professor of Department of Mathematics at Waseda University. When he was working at the Tsukuba University, he worked mainly on hyperbolic equations. After solving so called Finn’s starting problem in 1997 together with G.P. Galdi and J. Heywood, he has been working on the strong solutions of the initial boundary value problems of the Navier-Stokes equations. He obtained two big grants, Construction of mathematical analysis to investigate the fluid phenomena in the micro level and the macro level, 2012-2016 and A challenge to unsolved problems in fluid engineering modern mathematics analysis of the JST mathematics problem, 2009-2014. He was a leader of the Math-Phys unit of SGU program of Waseda University, 2016- 2020. He has organized international workshops on MFM every year since 2009. He is a distinguished professor of Cech Academy of Science, 2022/23.

Title: R solver approach to the maximal regularity and free bounary problem for the Navier Stokes equations

Abstract: First, I will talk about the R solver method created by myself to prove the maximal regularity for the initial-boundary problem with non-homogeneous boundary date. By using this method, I proved the Lp in time and Lq in space maximal regularity theorem for the Stokes equations with free boundary conditions. The idea of R solver is based on Weis operator valued Fourier multiplier theorem. As an application, I will talk about the local and global wellposedness of free boundary problem of the Navier-Stokes equations.