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 -