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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics