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

Shapiro, Victor L.

doi:10.1090/S0002-9947-1974-0380158-2

Isolated singularities for solutions of the nonlinear stationary Navier-Stokes equations
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by Victor L. Shapiro

Trans. Amer. Math. Soc. 187 (1974), 335-363

DOI: https://doi.org/10.1090/S0002-9947-1974-0380158-2

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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 $B(0,{r_0}) - \{ 0\}$ 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.

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