Abstract
The main theorem in this paper states that if a certan bound is imposed on the associated pressure pertaining to a weak solution of the Navier-Stokes equation then the solution is actually smooth. The proof uses the fact that such a bound implies a bound on the first derivatives of the solution which, in turn, leads to smoothness.
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References
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Kaniel, S. A sufficient condition for smoothness of solutions of Navier-Stokes equations. Israel J. Math. 6, 354–358 (1968). https://doi.org/10.1007/BF02771213
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DOI: https://doi.org/10.1007/BF02771213