On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity

Abstract

We study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.