Jou-chun Kuo (1nd year Doctor’s student, Department of Pure and Applied Mathematics)
1. Destination:
Institute of Mathematics, Czech Academy of Sciences (Prague, Czech Republic)
2. Period of Stay:
April 30, 2023~July 1, 2023
3. Purpose:
To attend the lectures given by Prof. Yoshihiro Shibata and study the Navier-Stokes equations and related topics.
4. Education and research activity at the destination:
During this stay, I attended two special lectures: “Maximal regularity and free boundary problem for the Navier-Stokes equations” and “R-solver approach to the maximal regularity of the free boundary problem for the Navier-Stokes equations” 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 “Biomedical Fluid Mechanics” workshop, ODE’s 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.
During 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<∞.
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- Prof. Yoshihiro Shibata’s lecture
5. Life in Czech (Prague):
According to an article I found on the internet, “Prague, the capital of the Czech Republic, has been voted the most beautiful city in the world.” I personally experienced this when I visited there. Prague is a very beautiful city, and when I went out for daily shopping or just to take a walk, I could always encounter some beautiful buildings. The accommodation and the Czech Academy of Sciences are located in bustling areas in Prague, which are called Praha 1 and 2. I often take a walk around on my way back home after leaving the Czech Academy of Sciences.
The food in the Czech Republic is meat cuisine with potatoes and a food called “dumpling”. When I first saw “dumpling” on the menu, I thought it was similar to dumpling as I had in Taiwan or Japan, but it’s actually more like bread (photo 1). On the first day I went to the Czech Academy of Sciences, I was taken to a restaurant near the institute (photo 2) for lunch. The food at that restaurant was really delicious, so I often had lunch there during my stay at the Czech Academy of Sciences. Also, I often had lunch with the members of the Czech Academy of Sciences. I had many conversations with them, and it became a great memory for me.
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- dumpling
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- Lunch
6. Other comments:
First and foremost, I would like to express my sincere gratitude to Prof. Nečasová Šárka for accepting my visit. I would also like to thank all the members I met at Czech Academy of Sciences for their support during my stay in Prague, as well as the postdoctoral researchers who always encouraged me and shared their research experiences. Finally, I would like to extend my deepest gratitude to Prof. Yoshihiro Shibata and Top Global University Project at Waseda University for giving me such a great opportunity to visit Czech Academy of Sciences. Moreover, I am also thankful to Ms. Yukari Ishizaki for making travel arrangements for me.
