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

• Autorzy: Stanislav Kračmar , Šárka Nečasová , Patrick Penel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 259-276

Daty

wydano

2008

Twórcy

autor

Stanislav Kračmar

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

autor

Šárka Nečasová

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

autor

Patrick Penel

• Department of Mathematics, Université de Sud Toulon-Var, B.P. 20132, 83957 La Garde Cedex, France

Identyfikatory

DOI

10.4064/bc81-0-17