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Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

For a bounded domain Ω n , n 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · u + p = f , div u = k , u | Ω = g with u L q , q n , and very general data classes for f , k , g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...

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