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Extrapolation of Sobolev imbeddings.

M. Krbec — 1997

Collectanea Mathematica

We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.

Weighted L² and L q approaches to fluid flow past a rotating body

R. FarwigS. KračmarM. KrbecŠ. NečasováP. Penel — 2009

Banach Center Publications

Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them...

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