Geodesic
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 547-558.

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We assume that ${\mathbb{v}}$ is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of ${\mathbb{v}}$ near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of ${\mathbb{v}}$.
DOI : 10.1023/B:APOM.0000024493.04008.06
Classification : 35B65, 35D10, 35Q30, 76D03, 76D05
Keywords: Navier-Stokes equations; regularity 
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Neustupa, Jiří. The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 547-558. doi : 10.1023/B:APOM.0000024493.04008.06. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024493.04008.06/

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