# Wydawnictwa / Banach Center Publications / Wszystkie tomy

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

### Tom 81 / 2008

Banach Center Publications 81 (2008), 259-276 MSC: Primary 76D05; Secondary 35Q30. DOI: 10.4064/bc81-0-17

#### Streszczenie

We consider the time-periodic Oseen flow around a rotating body in $\mathbb R^{3}$. 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 $-(\omega\wedge x)\cdot\nabla u+\omega\wedge u$ in the equation of momentum where $\omega$ denotes the angular velocity. We prove the existence of generalized weak solutions in $L^{q}$-space using Littlewood-Paley decomposition and maximal operators.

#### Autorzy

• Stanislav KračmarDepartment of Technical Mathematics
Karlovo nám. 13
121 35 Prague 2, Czech Republic
e-mail
• Šárka NečasováMathematical Institute of Academy of Sciences
Žitná 25
11567 Prague 1, Czech Republic
e-mail
• Patrick PenelDepartment of Mathematics
Université de Sud Toulon-Var
B.P. 20132
83957 La Garde Cedex, France
e-mail

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