On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases

Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the global well-posedness of semirelativistic equations with a power type nonlinearity on Euclidean spaces is studied. In two dimensional Hs scaling subcritical case with 1≤s≤2, the local well-posedness follows from a Strichartz estimate. In higher dimensional H1 scaling subcritical case, the local well-posedness for radial solutions follows from a weighted Strichartz estimate. Moreover, in three dimensional H1 scaling critical case, the local well-posedness for radial solutions follows from a uniform bound of solutions which may be derived by the corresponding one dimensional problem. Local solutions may be extended by a priori estimates.

Original languageEnglish
Pages (from-to)239-256
Number of pages18
JournalJournal des Mathematiques Pures et Appliquees
Volume136
DOIs
Publication statusPublished - 2020 Apr

Keywords

  • Global well-posedness
  • Scaling critical case
  • Scaling subcritical case
  • Semirelativistic equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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