Mikhail V. Korobkov

On the Morse-Sard property and level sets of Sobolev and BV functions.

We establish Luzin

Forward self-similar solutions of the Navier–Stokes equations in the half space

N

The Liouville Theorem for the Steady-State Navier–Stokes Problem for Axially Symmetric 3D Solutions in Absence of Swirl

and Morse-Sard properties for

The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings

BV_2

A bridge between Dubovitskiĭ–Federer theorems and the coarea formula

-functions defined on open domains in the plane. Using these results we prove that almost all level sets are finite disjoint unions of Lipschitz arcs whose tangent vectors are of bounded variation. In the case of

Leray’s Problem on Existence of Steady State Solutions for the Navier-Stokes Flow

W^{2,1}

Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains

-functions we strengthen the conclusion and show that almost all level sets are finite disjoint unions of

On the Flux Problem in the Theory of Steady Navier–Stokes Equations with Nonhomogeneous Boundary Conditions

C^1

On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn

-arcs whose tangent vectors are absolutely continuous.

Steady Navier–Stokes system with nonhomogeneous boundary conditions in the axially symmetric case

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.