A para-differential renormalization technique for nonlinear dispersive equations

Sebastian Herr, Alexandru D. Ionescu, Carlos E. Kenig, Herbert Koch

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

For α ∈ (1, 2) we prove that the initial-value problem {∂tu + Dαxu + ∂x(u2/2) = 0 on Rx × Rt; u(0) =, is globally well-posed in the space of real-valued L2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.

Original languageEnglish (US)
Pages (from-to)1827-1875
Number of pages49
JournalCommunications in Partial Differential Equations
Volume35
Issue number10
DOIs
StatePublished - Sep 15 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Dispersion generalized benjamin-ono equation
  • Frequencydependent renormalization
  • Global well-posedness
  • L initial data

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