SISSA Preprints

Singular Hartree equation in fractional perturbed Sobolev spaces

Show simple item record Michelangeli, Alessandro Olgiati, Alessandro Scandone, Raffaele 2017-11-14T10:26:30Z 2017-11-14T10:26:30Z 2017
dc.description.abstract We 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.language.iso en en_US
dc.relation.ispartofseries SISSA;52/2017/MATE
dc.subject Point interactions en_US
dc.subject Singular perturbations of the Laplacian en_US
dc.subject Regular and singular Hartree equation en_US
dc.subject Fractional singular Sobolev spaces en_US
dc.subject Strichartz estimates for point interaction en_US
dc.subject Hamiltonians Fractional Leibniz rule en_US
dc.subject Kato-Ponce commutator estimates
dc.title Singular Hartree equation in fractional perturbed Sobolev spaces en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 24 en_US

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