Nonexistence of isolated singularities for nonlinear systems of partial differential equations and some applications

Abstract

This paper deals with the singularities of solutions of several classes of nonlinear systems of partial differential equations appearing in gas dynamics and differential geometry. Our techniques depend principally on the method of microlocal analysis, for example microlocalized Sobolev spaces $H_{mcl}^{s}$ classical theory of the pseudodifferential operators and certainly the theory of paradifferential operators.