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

Stanislav 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 -