Remarks on infinite energy solutions of nonlinear wave equations

We first consider the existence of a solution of the critical semilinear wave equation in Besov space which extends the results in [P. Germain, Global infinite energy solutions of critical semilinear wave equation, Revista Matematica Iberoamericana 24 (2) (2008) 463-497] to general dimensions. Next we derive the existence and uniqueness of global solutions for a semilinear wave equation in Marcinkiewicz space.