Geodesic
Existence of global solutions for a parabolic
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 254-271

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In this note we consider an initial-boundary value problem describing a nonlinear variant of the nonstationary Stokes equation. We prove the existence of a (unique) global solution with Galerkin-type arguments. This result is not new but the method can be seen as an alternative to the technique presented for example in [7]. 
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     author = {M. Fuchs and G. A. Seregin},
     title = {Existence of global solutions for a parabolic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {254--271},
     publisher = {mathdoc},
     volume = {348},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a8/}
}
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M. Fuchs; G. A. Seregin. Existence of global solutions for a parabolic. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 254-271. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a8/