Existence of mild solutions for a Hamilton–Jacobi equation with critical fractional viscosity in the Besov spaces

Tsukasa Iwabuchi, Tatsuki Kawakami

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the Cauchy problem for the Hamilton–Jacobi equation with critical dissipation, ∂tu+(−Δ)1/2u=|∇u|p,x∈RN,t>0,u(x,0)=u0(x),x∈RN where p>1 and u0∈Br,11(RN)∩B∞,11(RN) with r∈[1,∞]. We show that for sufficiently small u0∈B˙∞,11(RN), there exists a global-in-time mild solution. Furthermore, we prove that the solution behaves asymptotically like suitable multiplies of the Poisson kernel.

Original languageEnglish
Pages (from-to)464-489
Number of pages26
JournalJournal des Mathematiques Pures et Appliquees
Volume107
Issue number4
DOIs
Publication statusPublished - 2017 Apr 1
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Fractional Laplacian
  • Hamilton–Jacobi equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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