Isolated singularities for solutions of the nonlinear stationary Navier-Stokes equations

Abstract

The notion for (u, p) to be a distribution solution of the nonlinear stationary Navier-Stokes equations in an open set is defined, and a theorem concerning the removability of isolated singularities for distribution solutions in the punctured open ball B ( 0 , r 0 ) − { 0 } B(0,{r_0}) - \{ 0\} is established. This result is then applied to the classical situation to obtain a new theorem for the removability of isolated singularities. In particular, in two dimensions this gives a better than expected result when compared with the theory of removable isolated singularities for harmonic functions.