arXiv subjects

Viktor Vyalov

Publications and source records attributed to Viktor Vyalov.

3 recordsLinked to original sources

arXiv2014

Estimates of solutions to the perturbed Stokes system

In this paper we derive local estimates of solutions of the Perturbed Stokes system. This system arises as a reduction of the Stokes system near a curved part of the boundary of the domain if one applies a diffeomorphism flatting the boundary. The estimates obtained in the paper play the crucial role in the investigation of partial regularity of weak solutions to the Navier-Stokes system near a curved part of the boundary of the domain.

math.AP↗

arXiv2012

On the Regularity of Weak Solutions to the Magneto Hydrodynamics System near the curved part of the boundary

We prove a sufficient conditions of local regularity of suitable weak solutions to the MHD system for the point from $C^3$-smooth part of the boundary. Our conditions are the generalizing of the Caffarelli--Kohn--Nirenberg theorem for Navier-Stokes equations.

math.AP↗

arXiv2011

On the local smoothness of weak solutions to the MHD system near the boundary

We prove some sufficient conditions of local regularity of the siutable weak solutions to the system of magnetohydrodynamics near the plane part of the boundary.

math.AP↗