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Remark on the scattering operator for the cubic nonlinear Dirac equation in three space dimensions.
- Source :
-
Journal of Differential Equations . Oct2015, Vol. 259 Issue 7, p3274-3297. 24p. - Publication Year :
- 2015
-
Abstract
- This paper is concerned with the scattering operator S for the three-dimensional Dirac equation with a cubic nonlinearity. It follows from known results that S is well-defined on a neighborhood of 0 in the Sobolev space H κ ( R 3 ; C 4 ) for any κ > 1 . In the present paper, we prove that for any M ∈ N and s ≥ max { κ , M } , there exists some neighborhood U of 0 in the weighted Sobolev space H s , M ( R 3 ; C 4 ) such that S ( U ) ⊂ H s , M ( R 3 ; C 4 ) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 259
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 103551882
- Full Text :
- https://doi.org/10.1016/j.jde.2015.04.020