On the singularities of solutions to 4-D semilinear dispersive wave equations

Abstract

In this note, we are concerned with the global singularity structures of weak solutions to 4-D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point. Combining Strichartz’s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal.