Japan. J. Math. 6, 121--141 (2011)

Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles

C. Kenig

Abstract: We discuss recent progress in the understanding of the global behavior of solutions to critical non-linear dispersive equations. The emphasis is on global existence, scattering and finite time blow-up. For solutions that are bounded in the critical norm, but which blow-up in finite time, we also discuss the issue of universal profiles at the blow-up time.


* This article is based on the 9th Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on June 4, 2011.