Geodesic
Estimates for solutions of the nonstationairy Stokes problem in anisotropic Sobolev spaces with mixed norm
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 124-150

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A new method is given to establish $L_{q,r}$-estimates for solutions of the nonstationary Stokes problem. The method is based on estimates for heat potentials in these spaces, and it is not connected with investigation of the resolvent for the Stokes operator. It is expected that the method is applicable to a wide class of parabolic initial boundary-value problems. Bibliography: 10 titles. 
@article{ZNSL_1995_222_a4,
     author = {P. Maremonti and V. A. Solonnikov},
     title = {Estimates for solutions of the nonstationairy {Stokes} problem in anisotropic {Sobolev} spaces with mixed norm},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--150},
     publisher = {mathdoc},
     volume = {222},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a4/}
}
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P. Maremonti; V. A. Solonnikov. Estimates for solutions of the nonstationairy Stokes problem in anisotropic Sobolev spaces with mixed norm. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 124-150. http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a4/