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Global existence of weak solutions to the non-linear Schrödinger equation with rough, time-dependent magnetic potentials

Raffaele Scandone
SISSA Trieste
Thursday, March 23, 2017 - 16:15

A challenging problem in Mathematical Physics and in Analysis of PDEs is to prove global well-posedness for the non-linear Schrödinger equation with magnetic potentials. In fact, even the properties of the linear problem are not totally understood. In particular, an important tool as the Strichartz estimates has been proved only under very restrictive assumption on the potentials. In this talk, after a brief overview of the known results, I will introduce the technique of parabolic regularization, which can be used to prove the existence of global weak solutions for the magnetic NLS under wide assumptions on the potential, which is allowed also to depend on time. Based on a recent work with Paolo Antonelli and Alessandro Michelangeli.

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