arXiv subjects

Bernard Nowakowski

Publications and source records attributed to Bernard Nowakowski.

3 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↗

arXiv2023

Global regular axially-symmetric solutions to the Navier-Stokes equations with small swirl

Axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and he angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.

math.AP↗

arXiv2013

Regularity criteria of weak solutions to NSE in some bounded domains involving the pressure

We present a short and elegant proof of an estimate for the pressure in terms of the velocity and external data in bounded domains under the slip and Navier boundary conditions. We also show an application of this result for conditional regularity of weak solutions to the Navier-Stokes equations.

math.AP↗