Global well-posedness for two dimensional semilinear wave equations

We consider the initial value problem (IVP) for certain semilinear wave equations in two dimensions. It is shown that global well-posedness holds in spaces of lower regularity than that suggested by the energy space H¹ x L²_x. The technique to be used is adapted from a general scheme originally introduced by J. Bourgain to establish global well posedness of the cubic nonlinear Schrödinger equation.