THE MODIFIED SCATTERING FOR DIRAC EQUATIONS OF SCATTERING-CRITICAL NONLINEARITY

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In this paper, we consider the Maxwell-Dirac system in 3 dimension under zero magnetic field. We prove the global well-posedness and modified scattering for small solutions in the weighted Sobolev class. Imposing the Lorenz gauge condition, (and taking the Dirac projection operator), it becomes a system of Dirac equations with Hartree type non -linearity with a long-range potential as |x|-1. We perform the weighted energy estimates. In this procedure, we have to deal with various resonance functions that stem from the Dirac projections. We use the space-time resonance argument of Germain-Masmoudi-Shatah ([14, 15, 16]), as well as the spinorial null-structure. On the way, we recognize a long-range interaction which is responsible for a logarithmic phase correction in the modified scattering statement. This result was obtained by Cloos in his dissertation [9], via a different technique (see Remark 1.2).
Publisher
KHAYYAM PUBL CO INC
Issue Date
2024-03
Language
English
Article Type
Article
Citation

ADVANCES IN DIFFERENTIAL EQUATIONS, v.29, no.3-4, pp.179 - 222

ISSN
1079-9389
DOI
10.57262/ade029-0304-179
URI
http://hdl.handle.net/10203/314533
Appears in Collection
MA-Journal Papers(저널논문)
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