On the Schrödinger–Boussinesq system with singular initial data

Abstract

We study the existence of local and global solutions for coupled Schrödinger–Boussinesq systems with initial data in weak-Lr spaces. These spaces contain singular functions with infinite L2-mass such as homogeneous functions of negative degree. Moreover, we analyze the self-similarity and radial symmetry of solutions by considering initial data with the right homogeneity and radially symmetric, respectively. Since functions in weak-Lr with r>2 have local finite L2-mass, the solutions obtained can be physically realized. Moreover, for initial data in Hs, local solutions belong to Hs which shows that the constructed data-solution map in weak-Lr recovers Hs-regularity.