Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials. (English) Zbl 1314.35119
Summary: We consider Schrödinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may not even be differentiable. The well-posedness of the Cauchy problem is proved in the frame of the modulation spaces, and results of micro-local propagation of singularities are given in terms of Gabor wave front sets.
MSC:
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35A18 | Wave front sets in context of PDEs |
| 35A21 | Singularity in context of PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35S30 | Fourier integral operators applied to PDEs |
| 42C15 | General harmonic expansions, frames |
| 47G30 | Pseudodifferential operators |
| 47D08 | Schrödinger and Feynman-Kac semigroups |
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