Electron. J. Diff. Eqns., Vol. 2005(2005), No. 45, pp. 1-11.

Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary

Zdenek Skalak

Any weak solution u of the Navier-Stokes equations in a bounded domain satisfying the Prodi-Serrin's conditions locally near the smooth boundary cannot have singular points there. This local-up-to-the-boundary boundedness of u in space-time implies the Holder continuity of u up-to-the-boundary in the space variables.

Submitted May 19, 2004. Published April 24, 2005.
Math Subject Classifications: 35Q35, 35B65.
Key Words: Navier-Stokes equations; weak solutions; boundary regularity.

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Zdenek Skalak
Czech Technical University
Faculty of Civil Engineering
Thakurova 7
166 29 Prague 6, Czech Republic
email: skalak@mat.fsv.cvut.cz

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