Interaction Equations for Short and Long Dispersive Waves

Daniella Bekiranov, Takayoshi Ogawa, Gustavo Ponce

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)

Abstract

We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction[formula]It is shown that for any initial data (u0,v0)∈Hs(R)×Hs-1/2(R) (s≥0), the solution for the above equation uniquely exists in a subset ofC((-T,T);Hs)×C((-T,T);Hs-1/2) and depends continuously on the data. By virtue of a special structure of the nonlinear coupling, the solution is stable under a singular limiting process.

Original languageEnglish
Pages (from-to)357-388
Number of pages32
JournalJournal of Functional Analysis
Volume158
Issue number2
DOIs
Publication statusPublished - 1998 Oct 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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