arXiv subjects

Wojciech Zajączkowski

Publications and source records attributed to Wojciech Zajączkowski.

2 recordsLinked to original sources

arXiv2023

On weighted estimates for the stream function of axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder

Higher-order estimates in weighted Sobolev spaces for solutions to a singular elliptic equation for the stream function in an axially symmetric cylinder are provided. These estimates are essential for investigating the existence of axially symmetric solutions to incompressible Navier-Stokes equations in axially symmetric cylinders. To derive the estimates the technique of Kondratiev is incorporated. The weight has a form of a power function of the distance to the axis of symmetry.

math.AP↗

arXiv2014

Stability of two-dimensional Navier-Stokes motions in the periodic case

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong three-dimensional solutions under the assumption that the initial data and the external force are sufficiently close to the initial data and the external force of the two-dimensional problem in appropriate spaces. The second result can be treated as stability of strong two-dimensional solutions in the set of suitably strong three-dimensional motions.

math.AP↗