# [M1 Seminar II] Week 8 : Lorentz Invariance of the Wave Equations

Edited by Leun Kim

Now we will introduce some lemmas for the proof of the global existence theorem for the nonlinear wave equations with quadratic nonlinearities. The exsistence theorem which was proven before gives $n >5$ for the quadratic nonlinearities. But in fact this is not optimal. The theorem which will be introduced in the next seminars shows that $n > 3$ is sufficient for this case. To prove this, we have to apply some lemmas using Lorentz group operators in the Minkowski space.

M1_Semi2_Week8

#### 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.