Wave seminar Radial solutions of supercritical wave equations in dimension 3

2014-12-12 16:30 - 2014-12-12 18:00
Faculty of Science Buliding #4 Room 501
Tristan Roy (Nagoya University)
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)