[M1 Seminar II] Week 4 : Regularities of the Solution and and Improved Existence Theorem

Edited by Leun Kim

We proved the right-continuity of the solution at the initial time in $W^{s,2}$ which implies the continuity of the whole interval. And by the PDE and Sobolev embedding theorem, we can easily get the regularity in the existence theorem. Also we can improve the theorem a little bit more. The theorem can be improved with respect to the length $T$ of the interval of existence, that is, the dependence on $\| u_0 \|_{s,2}, g_2$ can be weakened.



I was born and raised in Daegu, S. Korea. I majored in electronics and math in Seoul from 2007 to 2012. I've had a great interest in math since freshman year, and I studied PDE in Osaka, Japan from 2012-2014. I worked at a science museum and HUFS from 2014 in Seoul. Now I'm studying PDE in Tokyo, Japan. I also developed an interest in music, as I met a great piano teacher Oh in 2001, and joined an indie metal band in 2008. In my spare time, I enjoy various things, such as listening music, blogging, traveling, taking photos, and playing Go and Holdem. Please do not hesitate to contact me with comments, email, guestbook, and social medias.


  • 열심이시군요. 저는 요즘 abstract harmonic analysis를 하려는데 교재가 컴퓨터로 보기 매우 힘든 교재라 매우 골머리를 앓고 있습니다. 그런데 직접 사려면 15만원씩이나 들어서 이것도 참 골머리죠. ㅠ 아주 핵심적인 정리만 골라보는 형식으로 반정도 봤네요.

  • 뭐 특별한 건 아닙니다. 요즘 대수를 공부하고 있긴 하지만 저는 해석학쪽임이 분명하고 요즘 대수학을 많이 하고 있고 해석학은 평소대로 하는 만큼만 하고 있어서 그렇게 보일 뿐입니다. ㅋㅋ