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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Victor L. Shapiro
Journal: Trans. Amer. Math. Soc. 187 (1974), 335-363
MSC: Primary 35Q10
MathSciNet review: 0380158
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0380158-2
PII: S 0002-9947(1974)0380158-2
Keywords: Stationary Navier-Stokes equations, isolated singularities, nonlinear, distribution solution
Article copyright: © Copyright 1974 American Mathematical Society