{"id":26867,"date":"2023-10-02T10:05:02","date_gmt":"2023-10-02T01:05:02","guid":{"rendered":"https:\/\/www.waseda.jp\/inst\/sgu\/?p=26867"},"modified":"2023-12-28T14:29:39","modified_gmt":"2023-12-28T05:29:39","slug":"study-abroad-report-jou-chun-kuo-institute-of-mathematics-czech-academy-of-sciences-prague-czech-republic","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/10\/02\/26867\/","title":{"rendered":"Study Abroad Report: Jou-chun Kuo – Institute of Mathematics, Czech Academy of Sciences (Prague, Czech Republic)"},"content":{"rendered":"

Jou-chun Kuo <\/strong>(1nd year Doctor\u2019s student, Department of Pure and Applied Mathematics)<\/h3>\n

1. Destination:<\/h4>\n

Institute of Mathematics, Czech Academy of Sciences (Prague, Czech Republic)<\/p>\n

2. Period of Stay:<\/h4>\n

April 30, 2023~July 1, 2023<\/p>\n

3. Purpose:<\/h4>\n

To attend the lectures given by Prof. Yoshihiro Shibata and study the Navier-Stokes equations and related topics.<\/p>\n

\"\"<\/p>\n

4.\u00a0Education and research activity at the destination:<\/strong><\/h4>\n

During this stay, I attended two special lectures: \u201cMaximal regularity and free boundary problem for the Navier-Stokes equations\u201d and \u201cR-solver approach to the maximal regularity of the free boundary problem for the Navier-Stokes equations\u201d both of which were given by Prof. Yoshihiro Shibata. In these lectures, I was able to learn the maximal regularity approach to the Stokes equation and the applications to the free boundary problem. I also attended the \u201cBiomedical Fluid Mechanics\u201d workshop, ODE\u2019s seminar, and the lecture given by the postdoctoral researcher, Dr. Danica Basaric. The workshop is about mathematical modeling and various biomedical topics such as respiratory system and circulatory system.
\nDuring my stay at Czech Academy of Sciences, I completed the estimates of maximal L_1 regularity for the compressible Stokes equations under the guidance of Prof. Yoshihiro Shibata. We consider the generalized resolvent problem associated with the linearized system in the whole space and in the half-space. We used the real interpolation in order to overcome the difficulty when showing the case p=1 since we cannot rely on the Fourier multiplier theorem due to Weis that we usually apply to derive the maximal regularity theorem for case 1<p<\u221e.<\/p>\n\n\t\t