Japanese Journal of Mathematics

, Volume 6, Issue 2, pp 121–141

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

Special Feature: The Takagi Lectures

DOI: 10.1007/s11537-011-1108-0

Cite this article as:
Kenig, C. Jpn. J. Math. (2011) 6: 121. doi:10.1007/s11537-011-1108-0


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 equationglobal existencescatteringfinite time blow-upuniversal profiles

Mathematics Subject Classification (2010)


Copyright information

© The Mathematical Society of Japan and Springer Japan 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA