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Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials

Elena Cordero

Università di Torino, Dipartimento di Matematica, via Carlo Alberto 10, 10123 Torino, Italy

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Fabio Nicola

Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino, Italy

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, and

Luigi Rodino

Università di Torino, Dipartimento di Matematica, via Carlo Alberto 10, 10123 Torino, Italy

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https://doi.org/10.1142/S0129055X15500014Cited by:17 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 35A18, 35A21, 35B65, 35S30, 42C15, 47G30, 47D08

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