For nonlinear wave equations, we cannot guarantee that the solutions exist for some initial value problems. Also the global solutions may exist but also it may have some singularities depending on the initial conditions. Thus we need the global existence theorem to check these facts. We briefly introduce S. Klainerman’s results which was done in the middle of 1980’s.
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.