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Time Decay of Scaling Critical Electromagnetic Schrödinger Flows

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Abstract

We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp \({L^1 \to L^\infty}\) time decay estimate for the 3D-inverse square and the 2D-Aharonov–Bohm potentials.

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Authors and Affiliations

  1. SAPIENZA Università di Roma, P.le A. Moro 5, 00185, Rome, Italy

    Luca Fanelli

  2. Università di Milano Bicocca, Dipartimento di Matematica e applicazioni, Via Cozzi 53, 20125, Milan, Italy

    Veronica Felli

  3. ICMAT-CSIC, Ciudad Universitaria de Cantoblanco, 28049, Madrid, Spain

    Marco A. Fontelos & Ana Primo

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  1. Luca Fanelli
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  2. Veronica Felli
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  3. Marco A. Fontelos
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Correspondence to Luca Fanelli.

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Communicated by W. Schlag

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Fanelli, L., Felli, V., Fontelos, M.A. et al. Time Decay of Scaling Critical Electromagnetic Schrödinger Flows. Commun. Math. Phys. 324, 1033–1067 (2013). https://doi.org/10.1007/s00220-013-1830-y

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