TY - JOUR

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

AU - Fujiwara, Kazumasa

AU - Machihara, Shuji

AU - Ozawa, Tohru

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

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.

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U2 - 10.1007/s00220-015-2347-3

DO - 10.1007/s00220-015-2347-3

M3 - Article

AN - SCOPUS:84937763585

SN - 0010-3616

VL - 338

SP - 367

EP - 391

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -