### 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 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

**Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations.** / Fujiwara, Kazumasa; Machihara, Shuji; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 338, no. 1, pp. 367-391. https://doi.org/10.1007/s00220-015-2347-3

}

TY - JOUR

T1 - Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations

AU - Fujiwara, Kazumasa

AU - Machihara, Shuji

AU - Ozawa, Tohru

PY - 2015/8/1

Y1 - 2015/8/1

N2 - The local well-posedness for the Cauchy problem of a system of semirelativistic equations in one space dimension is shown in the Sobolev space Hs of order s ≥ 0. We apply the standard contraction mapping theorem by using Bourgain type spaces Xs,b. We also use an auxiliary space for the solution in L2 = H0. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

AB - The local well-posedness for the Cauchy problem of a system of semirelativistic equations in one space dimension is shown in the Sobolev space Hs of order s ≥ 0. We apply the standard contraction mapping theorem by using Bourgain type spaces Xs,b. We also use an auxiliary space for the solution in L2 = H0. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

UR - http://www.scopus.com/inward/record.url?scp=84937763585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937763585&partnerID=8YFLogxK

U2 - 10.1007/s00220-015-2347-3

DO - 10.1007/s00220-015-2347-3

M3 - Article

AN - SCOPUS:84937763585

VL - 338

SP - 367

EP - 391

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -