Education

10.1997 — Ph.D. (C.Sc.) in Mathematics and Physics («Differential Equations»)
Institution: St. Petersburg Department of Steklov Mathematical Institute
Thesis title: On the Regularity for Generalized Solutions to Mathematical Problems of the Plasticity Theory and the Theory of Non-Newtonian Fluids
Advisor: G.A. Seregin

02.1994 — M.Sc. in Engineering/Mathematics
Institution: Peter the Great St. Petersburg Polytechnic University

Scientific interests

PDEs, mathematical hydrodynamics, Navier–Stokes equations, mathematical physics.

Selected publications

1. G.A. Seregin and T.N. Shilkin. Liouville-type theorems for the Navier–Stokes equations. Russian Mathematical Surveys 73:4, 661–724, 2018. (Originally in Russian, published in Uspekhi Mat. Nauk 73:4, 103–170, 2018.)
2. N. Filonov and T. Shilkin. On some properties of weak solutions to elliptic equations with divergence-free drifts. In: Mathematical Analysis in Fluid Mechanics: Selected Recent Results (Contemporary Mathematics, Vol. 710), AMS, 2018, pp. 105–120.
3. G.A. Seregin and T.N. Shilkin. The local regularity theory for the Navier-Stokes equations near the boundary. In: Proceedings of the St. Petersburg Mathematical Society, Vol. XV: Advances in Mathematical Analysis of Partial Differential Equations, AMS, 2014, pp. 219–244.

Additional Information

See my curriculum vitae (in English) — also available here.

Teaching