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

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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 s of order s ≥ 0. We apply the standard contraction mapping theorem by using Bourgain type spaces X s,b. We also use an auxiliary space for the solution in L 2 = H 0. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

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Authors and Affiliations

  1. Department of Pure and Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kazumasa Fujiwara

  2. Faculty of Science, Saitama Univeristy, 255 Shimo-Okubo, Saitama, 338-8570, Japan

    Shuji Machihara

  3. Department of Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Tohru Ozawa

Authors
  1. Kazumasa Fujiwara
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  2. Shuji Machihara
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  3. Tohru Ozawa
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Correspondence to Kazumasa Fujiwara.

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Communicated by W. Schlag

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Fujiwara, K., Machihara, S. & Ozawa, T. Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations. Commun. Math. Phys. 338, 367–391 (2015). https://doi.org/10.1007/s00220-015-2347-3

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  • DOI: https://doi.org/10.1007/s00220-015-2347-3

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