TY - RPRT
T1 - The Singular Hartree Equation in Fractional Perturbed Sobolev Spaces
Y1 - 2017
A1 - Alessandro Michelangeli
A1 - Alessandro Olgiati
A1 - Raffaele Scandone
AB - 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 SchrÃ¶dinger 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.
UR - http://preprints.sissa.it/handle/1963/35301
U1 - 35607
U2 - Mathematics
U4 - 1
ER -