On the Schrödinger–Boussinesq system with singular initial data

We study the existence of local and global solutions for coupled Schrödinger–Boussinesq systems with initial data in weak- L r spaces. These spaces contain singular functions with infinite L 2 -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- L r with r > 2 have local finite L 2 -mass, the solutions obtained can be physically realized. Moreover, for initial data in H s , local solutions belong to H s which shows that the constructed data-solution map in weak- L r recovers H s -regularity.