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

R. Farwig; S. Kračmar; M. Krbec; Š. Nečasová; P. Penel

Banach Center Publications (2009)

- Volume: 86, Issue: 1, page 59-81
- ISSN: 0137-6934

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topR. Farwig, et al. "Weighted L² and $L^{q}$ approaches to fluid flow past a rotating body." Banach Center Publications 86.1 (2009): 59-81. <http://eudml.org/doc/282322>.

@article{R2009,

abstract = {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.},

author = {R. Farwig, S. Kračmar, M. Krbec, Š. Nečasová, P. Penel},

journal = {Banach Center Publications},

keywords = {variational approach; Littlewood-Paley theory; stationary Oseen flow; weighted estimates},

language = {eng},

number = {1},

pages = {59-81},

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

url = {http://eudml.org/doc/282322},

volume = {86},

year = {2009},

}

TY - JOUR

AU - R. Farwig

AU - S. Kračmar

AU - M. Krbec

AU - Š. Nečasová

AU - P. Penel

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

JO - Banach Center Publications

PY - 2009

VL - 86

IS - 1

SP - 59

EP - 81

AB - 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.

LA - eng

KW - variational approach; Littlewood-Paley theory; stationary Oseen flow; weighted estimates

UR - http://eudml.org/doc/282322

ER -

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