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New regularity results for a generic model equation in exterior 3D domains. (English) Zbl 1101.35350
Mucha, Piotr (ed.) et al., Regularity and other aspects of the Navier-Stokes equations. Based on the conference on regularity and other qualitative aspects of the Navier-Stokes equations, Bȩdlewo, Poland, August 31–September 6, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 70, 139-155 (2005).
Summary: 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 [S. Kračmar and P. Penel, Funkcial Ekvac. 47, 499–523 (2004)]. 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.
For the entire collection see [Zbl 1081.35003].

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J20 Variational methods for second-order elliptic equations