The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space

Jun ichi Segata, Keishu Watanabe

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the generalized Korteweg-de Vries (gKdV) equation with the time oscillating nonlinearity: ∂tu + ∂x 3u + g(ωt)∂x(│u│p−1u) = 0, (t, x) ∈ R × R. Under the suitable assumption on g, we show that if the nonlinear term is mass critical or supercritical i.e., p≥ 5 and u(0)∈Ḣsp , where sp= 1 / 2 - 2 / (p- 1) is a scale critical exponent, then there exists a unique global solution to (gKdV) provided that | ω| is sufficiently large. We also obtain the behavior of the solution to (gKdV) as │ ω │ → ∞.

Original languageEnglish
Article number51
JournalNonlinear Differential Equations and Applications
Volume23
Issue number5
DOIs
Publication statusPublished - Oct 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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