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Global existence of solutions to Navier-Stokes equations in cylindrical domains

100%

Nowakowski B., Zajączkowski W.

Applicationes Mathematicae

2009

tom 36

nr 2

169-182

We prove the existence of global and regular solutions to the Navier-Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the x₃-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval [0,T], where T > 0 is large, on the assumption that the L₂-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the direction of the axis of the cylinder are small. In this paper we continue the solution to all times.

Global attractor for Navier-Stokes equations in cylindrical domains

100%

Nowakowski B., Zajączkowski W.

Applicationes Mathematicae

2009

tom 36

nr 2

183-194

Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder. With the same assumptions we prove in this paper the existence of a global attractor for the Navier-Stokes equations and convergence of solutions to the stationary solutions for the large viscosity coefficient.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Nowakowski B.

2 Zajączkowski W.

2 2009

Wyniki wyszukiwania

Global existence of solutions to Navier-Stokes equations in cylindrical domains

Global attractor for Navier-Stokes equations in cylindrical domains