Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

Fernando Bernal-Vílchis, Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂ x ∂ t u - b / 3 ∂ x 3 u - ∂ x K u 3 = a u, t, x ℝ 2, u 0, x = u 0 x, xR, where a b > 0. Define 0 = 27 a / b 1 / 4. Suppose that K is a pseudodifferential operator with a symbol K ^ such that K ^ ± 0 = 0, I mK ^ = 0, and K ^ ≤ C. For example, we can take K^ = 2 - 0 2 / 2 + 1. We prove the global in time existence and the large time asymptotic behavior of solutions.

Original languageEnglish
Article number3879017
JournalInternational Journal of Differential Equations
Volume2017
DOIs
Publication statusPublished - 2017
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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