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On mass concentration for the critical generalized Korteweg–de Vries equation

Published online by Cambridge University Press:  17 December 2015

B. Pigott
B. Pigott*
Affiliation:
Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA (pigottbj@wfu.edu)
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Abstract

We show that blow-up solutions of the critical generalized Korteweg–de Vries equation in H1() concentrate at least the mass of the ground state at the blow-up time. The I-method is used to prove a slightly weaker result in Hs() with 16/17 < s < 1. Under an assumption on the precise blow-up rate, we are able to use similar arguments to prove a more precise analogue of the H1() concentration result over the same range of s.

Keywords

Korteweg–de Vries (KdV) equationcritical normmass concentrationblow-upPrimary 35Q53
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 519 - 532
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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