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New regularity results for a generic model equation in exterior 3D domains

Stanislav Kračmar;  Patrick Penel — 2005

Banach Center Publications

We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.

L q -approach to weak solutions of the Oseen flow around a rotating body

Stanislav Kračmar;  Šárka Nečasová;  Patrick Penel — 2008

Banach Center Publications

We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in L q -spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions in L q -space...

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