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Wojciech Zajaczkowski

Publications and source records attributed to Wojciech Zajaczkowski.

7 recordsLinked to original sources
arXiv2015

Stability of two-dimensional solutions to the Navier-Stokes equations in cylindrical domains under Navier-boundary conditions

The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time. Assuming that the initial velocity and the external force are sufficiently close to the initial velocity and the external force of the two-dimensional solutions we prove global existence of three-dimensional solutions which remain close to the two-dimensional solutions for all time. In this way we mean stability of two-dimensional solutions.

math.AP↗
arXiv2013

Global regular axially symmetric solutions to the Navier-Stokes equations

The existence of global regular axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder is proved. The main step in the proof is a proof of the Holder continuity of the swirl. This gives a possibility to prove global a priori estimate for regular solutions. Then a local solution can be extended step by step in time.

math.AP↗
arXiv2010

Existence of global weak solutions for Navier-Stokes equations with large flux

Global existence of weak solutions to the Navier-Stokes equation in a cylindrical domain under the slip boundary conditions and with inflow and outflow was proved. To prove the energy estimate, crucial for the proof, we use the Hopf function. This makes us possible to derive such estimate that the inflow and outflow must not vanish as t converges to infinity. The proof requires estimates in weighted Sobolev spaces for solutions to the Poisson equation. Finally, the paper is the first step to prove the existence of global regular special solutions to the Navier-Stokes equations with inflow and outflow.

math.AP↗