01292nas a2200157   4500008004100000245006900041210006900110260002100179300001200200490000700212520078900219100002901008700002401037700002301061856005001084       2018                        eng d00aSingular Hartree equation in fractional perturbed Sobolev spaces0 aSingular Hartree equation in fractional perturbed Sobolev spaces  bTaylor & Francis  a558-5880 v253 a<p>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 point-like 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.</p>1 aMichelangeli, Alessandro1 aOlgiati, Alessandro1 aScandone, Raffaele  uhttps://doi.org/10.1080/14029251.2018.1503423