# ${L}^{q}$-approach to weak solutions of the Oseen flow around a rotating body

Stanislav Kračmar; Šárka Nečasová; Patrick Penel

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 259-276
- ISSN: 0137-6934

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topStanislav Kračmar, Šárka Nečasová, and Patrick Penel. "$L^q$-approach to weak solutions of the Oseen flow around a rotating body." Banach Center Publications 81.1 (2008): 259-276. <http://eudml.org/doc/282166>.

@article{StanislavKračmar2008,

abstract = {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 using Littlewood-Paley decomposition and maximal operators.},

author = {Stanislav Kračmar, Šárka Nečasová, Patrick Penel},

journal = {Banach Center Publications},

keywords = {Bogovskii operator; existence; Littlewood-Paley decomposition},

language = {eng},

number = {1},

pages = {259-276},

title = {$L^q$-approach to weak solutions of the Oseen flow around a rotating body},

url = {http://eudml.org/doc/282166},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Stanislav Kračmar

AU - Šárka Nečasová

AU - Patrick Penel

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

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 259

EP - 276

AB - 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 using Littlewood-Paley decomposition and maximal operators.

LA - eng

KW - Bogovskii operator; existence; Littlewood-Paley decomposition

UR - http://eudml.org/doc/282166

ER -

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