Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles
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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 Phrasescritical non-linear dispersive equation global existence scattering finite time blow-up universal profiles
Mathematics Subject Classification (2010)35L52 35Q53 35Q55
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