On uniqueness for supercritical nonlinear wave and Schrödinger equations

Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

In a recent paper [39], Struwe considered the Cauchy problem for a class of nonlinear wave and Schrödinger equations. Under some assumptions on the nonlinearities, it was shown that uniqueness of classical solutions can be obtained in the much larger class of distribution solutions satisfying the energy inequality. As pointed out in [39], the conditions on the nonlinearities are satisfied for any polynomial growth but they fail to hold for higher growth (for example eu2). Our aim here is to improve Struwe's result by showing that uniqueness holds for more general nonlinearities including higher growth or oscillations.

Original languageEnglish (US)
Pages (from-to)2386-2405
Number of pages20
JournalInternational Mathematics Research Notices
Volume2015
Issue number9
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)

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