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

作者：Fujiwara Kazumasa^*; Machihara Shuji; Ozawa Tohru

来源：Communications in Mathematical Physics, 2015, 338(1): 367-391.

DOI：10.1007/s00220-015-2347-3

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,X-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.

• 出版日期2015-8