Geodesic
Estimates of solutions of the second initial-boundary problem for the Stokes system in the spaces of functions with H\"older continuous derivatives with respect to spatial variables
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 254-279

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It is known that the solutions of parabolic initial boundary-value problems can be estimates in the Hölder norms with respect to the spatial variables for any fixed positive value of time in terms of similar norms of the data. We obtain estimate of this type for the solutions on nonstationary Stokes equations with stresses prescribed on the boundary. 
@article{ZNSL_1999_259_a12,
     author = {V. A. Solonnikov},
     title = {Estimates of solutions of the second initial-boundary problem for the {Stokes} system in the spaces of functions with {H\"older} continuous derivatives with respect to spatial variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {254--279},
     publisher = {mathdoc},
     volume = {259},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a12/}
}
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V. A. Solonnikov. Estimates of solutions of the second initial-boundary problem for the Stokes system in the spaces of functions with H\"older continuous derivatives with respect to spatial variables. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 254-279. http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a12/