Weighted L² and $L^{q}$ approaches to fluid flow past a rotating body

• Autorzy: R. Farwig , S. Kračmar , M. Krbec , Š. Nečasová , P. Penel
• Języki publikacji: EN

Abstrakty

EN

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 is based on a variational method in L²-spaces with weights reflecting the anisotropic behaviour of the Oseen fundamental solution. The other approach uses weighted multiplier theory, interpolation and Littlewood-Paley theory to get a priori estimates in anisotropically weighted $L^{q}$-spaces.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 59-81

Daty

wydano

2009

Twórcy

autor

R. Farwig

• Department of Mathematics, Darmstadt University of Technology, 64289 Darmstadt, Germany

autor

S. Kračmar

• Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35 Prague 2, Czech Republic

autor

M. Krbec

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Prague 1, Czech Republic

autor

Š. Nečasová

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Prague 1, Czech Republic

autor

P. Penel

• Université du Sud Toulon-Var, Mathématiques, B.P. 20132, 83957 La Garde Cedex, France

Identyfikatory

DOI

10.4064/bc86-0-4