19 citations · 32 across the 9 of their papers we have counts for
9 papers
On the --stability for parabolic equations with a supercritical drift term
Mikhail Glazkov, Timofey Shilkin
In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic…
On the existence and uniqueness of weak solutions to elliptic equations with a singular drift
Misha Chernobai, Tim Shilkin
In this paper we study the Dirichlet problem for a scalar elliptic equation in a bounded Lipschitz domain with a singular drift of the form $b_0= b-α\frac {x…
Elliptic equations with a singular drift from a weak Morrey space
Misha Chernobai, Timofey Shilkin
In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift satisfying in $…
Scalar elliptic equations with a singular drift
Misha Chernobai, Timofey Shilkin
We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation in a bounded domain $Ω…
On some properties of weak solutions to elliptic equations with divergence-free drifts
Nikolay Filonov, Timofey Shilkin
We discuss the local properties of weak solutions to the equation . The corresponding theory is well-known in the case , where is the dimensio…
Remarks on Liouville Type Theorems for Steady-State Navier-Stokes Equations
Gregory Seregin
Liouville type theorems for the stationary Navier-Stokes equations are proven under certain assumptions. These assumptions are motivated by conditions that appear in Liouvile type…
The local regularity theory for the Navier-Stokes Equations Near the Boundary
Gregory Seregin, Timofey Shilkin
This is an expository paper on the theory of local regularity for weak solutions to the non-stationary 3D Navier-Stokes equations near the boundary of a domain.
On the Boundary Regularity of Weak Solutions to the MHD System
V. Vyalov, T. Shilkin
We prove the partial regularity of the boundary suitable weak solutions to the MHD system near the plane part of the boundary.
On the Stokes problem with non-zero divergence
Nikolay Filonov, Tim Shilkin
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.