Global wellposedness for a one-dimensional Chern–Simons–Dirac system in Lp

Shuji Machihara, Takayoshi Ogawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The global wellposedness in Lp(ℝ) for the Chern–Simons–Dirac equation in the 1+1 space and time dimension is discussed. We consider two types of quadratic nonlinearity: the null case and the non-null case. We show the time global wellposedness for the Chern–Simon–Dirac equation in the framework of Lp(ℝ), where 1≤p≤∞ for the null case. For the scaling critical case, p = 1, mass concentration phenomena of the solutions may occur in considering the time global solvability. We invoke the Delgado–Candy estimate which plays a crucial role in preventing concentration phenomena of the global solution. Our method is related to the original work of Candy (2011), who showed the time global wellposedness for the single Dirac equation with cubic nonlinearity in the critical space L2(ℝ).

Original languageEnglish
Pages (from-to)1175-1198
Number of pages24
JournalCommunications in Partial Differential Equations
Volume42
Issue number8
DOIs
Publication statusPublished - 2017 Aug 3

Keywords

  • Chern–Simons–Dirac equation
  • global wellposedness
  • mass concentration phenomena

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Global wellposedness for a one-dimensional Chern–Simons–Dirac system in L<sup>p</sup>'. Together they form a unique fingerprint.

  • Cite this