### Abstract

The local well-posedness for the Cauchy problem of a system of semirelativistic equations in one space dimension is shown in the Sobolev space H<sup>s</sup> of order s ≥ 0. We apply the standard contraction mapping theorem by using Bourgain type spaces X<sup>s,b</sup>. We also use an auxiliary space for the solution in L<sup>2</sup> = H<sup>0</sup>. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

Original language | English |
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Pages (from-to) | 367-391 |

Number of pages | 25 |

Journal | Communications in Mathematical Physics |

Volume | 338 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Aug 1 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Fujiwara, K., Machihara, S., & Ozawa, T. (2015). Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations.

*Communications in Mathematical Physics*,*338*(1), 367-391. https://doi.org/10.1007/s00220-015-2347-3