Geodesic
Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions
Electronic journal of differential equations, Tome 1999 (1999)
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin three-dimensional domain with periodic boundary conditions has global regularity, as long as there is some control on the size of the initial data and the forcing term, where the control is larger than that obtainable via "small data" estimates. The approach taken is to consider the three-dimensional equation as a perturbation of the equation when the vector field does not depend upon the coordinate in the thin direction.
Classification : 35Q30, 76D05, 35B65
Keywords: Navier-Stokes equation, thin domain 
@article{EJDE_1999__1999__a47,
     author = {Montgomery-Smith,  Stephen},
     title = {Global regularity of the {Navier-Stokes} equation on thin three-dimensional domains with periodic boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0923.35120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a47/}
}
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%A Montgomery-Smith,  Stephen
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%J Electronic journal of differential equations
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Montgomery-Smith,  Stephen. Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a47/