Singular Hartree equation in fractional perturbed Sobolev spaces

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dc.contributor.areaMathematicsen_US
dc.contributor.authorMichelangeli, Alessandro
dc.contributor.authorOlgiati, Alessandro
dc.contributor.authorScandone, Raffaele
dc.date.accessioned2017-11-14T10:26:30Z
dc.date.available2017-11-14T10:26:30Z
dc.date.issued2017
dc.description.abstractWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed pointlike impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35301
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;52/2017/MATE
dc.relation.lastpage24en_US
dc.subjectPoint interactionsen_US
dc.subjectSingular perturbations of the Laplacianen_US
dc.subjectRegular and singular Hartree equationen_US
dc.subjectFractional singular Sobolev spacesen_US
dc.subjectStrichartz estimates for point interactionen_US
dc.subjectHamiltonians Fractional Leibniz ruleen_US
dc.subjectKato-Ponce commutator estimates
dc.titleSingular Hartree equation in fractional perturbed Sobolev spacesen_US
dc.typePreprinten_US
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