Geodesic
$L_{3,\infty}$-solutions to the 3D-Navier--Stokes system in the domain with a~curved boundary
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 133-152

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We show that $L_{3,\infty}$-solutions to the three-dimensional Navier–Stokes equations near the curved smooth part of the boundary are Hölder continuous. The corresponding result near the plane part of the boundary was obtained earlier by G. Seregin. 
@article{ZNSL_2006_336_a6,
     author = {A. S. Mikhailov and T. N. Shilkin},
     title = {$L_{3,\infty}$-solutions to the {3D-Navier--Stokes} system in the domain with a~curved boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--152},
     publisher = {mathdoc},
     volume = {336},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a6/}
}
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A. S. Mikhailov; T. N. Shilkin. $L_{3,\infty}$-solutions to the 3D-Navier--Stokes system in the domain with a~curved boundary. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 133-152. http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a6/