Wyniki wyszukiwania

1

The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity

100%

Neustupa J., Penel P.

Banach Center Publications

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2008

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tom 81

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nr 1

321-335

EN

We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.

2

Estimates up to the boundary of a weak solution to the Navier-Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor

100%

Neustupa J., Penel P.

Banach Center Publications

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2005

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tom 70

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nr 1

185-197

EN

We formulate sufficient conditions for regularity up to the boundary of a weak solution v in a subdomain Ω × (t₁,t₂) of the time-space cylinder Ω × (0,T) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that Ω is a cube.

3

New regularity results for a generic model equation in exterior 3D domains

100%

Kračmar S., Penel P.

Banach Center Publications

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2005

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tom 70

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nr 1

139-155

EN

We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.

4

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

81%

Kračmar S., Nečasová Š., Penel P.

Banach Center Publications

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2008

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tom 81

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nr 1

259-276

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.

Ograniczanie wyników

4 Banach Center Publications

4 Penel P.

2 Kračmar S.

2 Neustupa J.

1 Nečasová Š.

2 2008

2 2005

The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity

Estimates up to the boundary of a weak solution to the Navier-Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor

New regularity results for a generic model equation in exterior 3D domains

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