Geodesic
Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 619-639.

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In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin's type on velocity ${\bold v}$ and pressure $p$ under which $({\bold x}_0,t_0)\in \Omega \times (0,T)$ is a regular point of ${\bold v}$. The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex $({\bold x}_0,t_0)$ and the axis parallel with the $t$-axis.
Classification : 35B65, 35Q10, 35Q30, 76D05
Keywords: Navier-Stokes equations; suitable weak solutions; local regularity 
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     author = {Skal\'ak, Zden\v{e}k},
     title = {Conditions of {Prodi-Serrin's} type for local regularity of suitable weak solutions to the {Navier-Stokes} equations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {619--639},
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     volume = {43},
     number = {4},
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     mrnumber = {2045785},
     zbl = {1090.35148},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a3/}
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Skalák, Zdeněk. Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 619-639. http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a3/