Geodesic
Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 35Q35, 35B65
Keywords: Navier-Stokes equations, weak solutions, boundary regularity 
@article{EJDE_2005__2005__a287,
     author = {Skalak,  Zdenek},
     title = {Regularity of weak solutions of the {Navier-Stokes} equations near the smooth boundary},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1070.35025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a287/}
}
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Skalak,  Zdenek. Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a287/