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

Kazumasa Fujiwara, Shuji Machihara, Tohru Ozawa

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)367-391
    Number of pages25
    JournalCommunications in Mathematical Physics
    Volume338
    Issue number1
    DOIs
    Publication statusPublished - 2015 Aug 1

    Fingerprint

    Cauchy problem
    Well-posedness
    System of equations
    Cauchy Problem
    Sobolev space
    Contraction Mapping
    Local Well-posedness
    Global Well-posedness
    conservation laws
    regularity
    Persistence
    Conservation Laws
    Sobolev Spaces
    contraction
    theorems
    Regularity
    Theorem

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

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

    In: Communications in Mathematical Physics, Vol. 338, No. 1, 01.08.2015, p. 367-391.

    Research output: Contribution to journalArticle

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