Analyticity and smoothing effect for the Korteweg de Vries equation with a single point singularity

Keiichi Kato, Takayoshi Ogawa

研究成果: Article査読

25 被引用数 (Scopus)

抄録

We show that a solution of the Cauchy problem for the KdV equation, {∂tυ + ∂3xυ + ∂x2) = 0, t ∈ (-T, T), x ∈ ℝ, υ(0, x) = φ(x). has a drastic smoothing effect up to real analyticity if the initial data only have a single point singularity at x = 0. It is shown that for Hs(ℝ) (s > -3/4) data satisfying the condition (equation presented) the solution is analytic in both space and time variable. The above condition allows us to take as initial data the Dirac δ measure or the Cauchy principal value of 1/x. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [20] and a systematic use of the dilation generator 3t∂t + x∂x.

本文言語English
ページ(範囲)577-608
ページ数32
ジャーナルMathematische Annalen
316
3
DOI
出版ステータスPublished - 2000 3
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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