# [M1 Seminar II] Week 6 : Weighted a priori Estimates for Small Data

Edited by Leun Kim

For the proof of the global existence theorem of nonlinear wave equations, this a priori estimates is essential as well as the high energy estimates. Also the high energy estimates play an important role in the proof of a priori estimates. For this purpose, we have used $L^p-L^q$ decay estimates for the linear wave equations.

M1_Semi2_Week6

#### Leun Kim

Ph.D Candidate at The University of Tokyo
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.