Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589643 | Journal of Functional Analysis | 2016 | 52 Pages |
Abstract
We consider the Cauchy problem for a quadratic derivative nonlinear Schrödinger system in Sobolev space HsHs. In this paper, under the null condition and the mass resonance relation, we prove large data local well-posedness if the space dimension d≥3d≥3 and s≥scs≥sc, d=2d=2 and s>scs>sc or d=1d=1 and s≥0s≥0, where scsc is the scaling critical regularity. Moreover, under the same assumptions, we also prove small data global well-posedness and scattering in HsHs, if d≥3d≥3 and s≥scs≥sc. Our proof is based on a contraction argument using the UpUp and VpVp type function spaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Masahiro Ikeda, Nobu Kishimoto, Mamoru Okamoto,