Special Feature: The Takagi Lectures

Japanese Journal of Mathematics

, Volume 6, Issue 2, pp 121-141

First online:

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

  • Carlos KenigAffiliated withDepartment of Mathematics, University of Chicago Email author 

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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.

Keywords and Phrases

critical non-linear dispersive equation global existence scattering finite time blow-up universal profiles

Mathematics Subject Classification (2010)

35L52 35Q53 35Q55