T. Shilkin

Regularity of Stationary Weak Solutions in the Theory of Generalized Newtonian Fluids with Energy Transfer

In this paper, we prove regularity results for weak solutions to some stationary problems arising in the theory of generalized Newtonian fluids with energy transfer. Namely, we prove that these solutions are strong. In the two-dimensional case, we prove the Hölder continuity of the first gradient of a solution. Bibliography: 30 titles.

On Coercive Estimates for Solutions of Linear Systems of Hydrodynamic Type

Local and nonlocal coercive estimates in Lebesgue, Hölder, and Morrey–Campanato spaces are proved for solutions of linear stationary systems of hydrodynamic type. For this purpose, the technique proposed by Italian mathematicians for the study of solutions to equations and systems of elliptic and parabolic types is developed. Bibliography: 14 titles.

On the Stokes problem with nonzero divergence

The strong solvability of the nonstationary Stokes problem with nonzero divergence in a bounded domain is studied. Bibliography: 12 titles.

A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity

A p-Laplacian flow (1 < p < ∞) with nonlocal diffusivity is obtained as an asymptotic limit case of a high thermal conductivity flow described by a coupled system involving the dissipation energy.