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

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

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...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 338; no. 1; pp. 367 - 391
Main Authors: Fujiwara, Kazumasa, Machihara, Shuji, Ozawa, Tohru
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2015
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Cauchy Problem
Auxiliary Space
Bilinear Estimate
Strichartz Estimate
Closed Linear Subspace
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-015-2347-3