## 波動セミナー Radial solutions of supercritical wave equations in dimension 3

2014年 　 12月 12日 16時 30分 ～ 2014年 　 12月 12日 18時 00分

Tristan Roy（名古屋大学高等研究院／多元数理科学研究科）

In this talk we are interested in the radial solutions of semilinear wave equations with a supercritical nonlinearity, in dimension 3, and with initial data lying in the critical Sobolev space. It is well-known that one can construct solutions on a short time interval. Then next question is: what is the asymptotic behavior of these solutions? In other words do the solutions behave like free solutions or is there blow-up? In the latter case, the standard blow-up criterion says that a Strichartz-type norm must explode. In this talk we upgrade the standard blow-up criterion. We prove that if there is blow-up, then the critical Sobolev norm must also explode. (in collaboration with Thomas Duyckerts)