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critical norm

Proceedings of the Edinburgh Mathematical Society (1)

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On mass concentration for the critical generalized Korteweg–de Vries equation
B. Pigott
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 2 / May 2016

Published online by Cambridge University Press:

17 December 2015, pp. 519-532
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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.