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

Stanislav KračmarŠárka NečasováPatrick Penel — 2008

Banach Center Publications

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...

Shape Sensitivity Analysis of the Dirichlet Laplacian in a Half-Space

Cherif AmroucheŠárka NečasováJan Sokołowski — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.

The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics

Eduard FeireislŠárka Matušů-Nečasová — 2011

Applications of Mathematics

The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

On the linear problem arising from motion of a fluid around a moving rigid body

Šárka Matušů-NečasováJörg Wolf — 2015

Mathematica Bohemica

We study a linear system of equations arising from fluid motion around a moving rigid body, where rotation is included. Originally, the coordinate system is attached to the fluid, which means that the domain is changing with respect to time. To get a problem in the fixed domain, the problem is rewritten in the coordinate system attached to the body. The aim of the present paper is the proof of the existence of a strong solution in a weighted Lebesgue space. In particular, we prove the existence...

Bipolar Barotropic Non-Newtonian Compressible Fluids

Šárka Matušu-NečasováMária Medviďová-Lukáčová — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We are interested in a barotropic motion of the non-Newtonian bipolar fluids . We consider a special case where the stress tensor is expressed in the form of potentials depending on and ( e i j x k ) . We prove the asymptotic stability of the rest state under the assumption of the regularity of the potential forces.

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