Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

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dc.contributor.areaMathematicsen_US
dc.contributor.authorAntonelli, Paolo
dc.contributor.authorMichelangeli, Alessandro
dc.contributor.authorScandone, Raffaele
dc.date.accessioned2017-09-11T11:03:35Z
dc.date.available2017-09-11T11:03:35Z
dc.date.issued2017
dc.description.abstractWe prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.en_US
dc.identifier.sissaPreprint17/2017/MATE
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35294
dc.language.isoenen_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;17/2017/MATE
dc.relation.lastpage36en_US
dc.subjectNon-linear Schrödinger equationen_US
dc.subjectMagnetic potentialsen_US
dc.subjectViscosity regularisationen_US
dc.subjectStrichartz estimatesen_US
dc.subjectWeak solutionsen_US
dc.titleGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentialsen_US
dc.typePreprinten_US
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