Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows

S Ershkov, N Burmasheva, DD Leshchenko… - Symmetry, 2023 - mdpi.com
We present a new exact solution of the thermal diffusion equations for steady-state shear
flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale …

Optimal boundary control of nonlinear-viscous fluid flows

ES Baranovskii - Sbornik: Mathematics, 2020 - iopscience.iop.org
The optimal control problem for a stationary model of a nonlinear-viscous incompressible
fluid flowing through a bounded domain is considered under the wall slip condition. As a …

Hölder continuity of solutions for unsteady generalized Navier–Stokes equations with p (x, t)-power law in 2D

C Sin, ES Baranovskii - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
We prove Hölder continuity of gradient of a unique weak solution for unsteady generalized
Navier–Stokes equations with p (x, t)-power law with Dirichlet type boundary condition under …

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

S Ershkov, E Prosviryakov… - … Methods in the …, 2023 - Wiley Online Library
In this semianalytical research, we present a new ansatz in solving the Störmer problem with
numerical findings in graphical representations of solutions where dynamics of the charged …

Heat Transfer Investigation in Plus-Shaped Enclosure Using Power Law Fluid: A Finite Element Approach

IS Chuhan, J Li, Z Guo, M Yaqub, MA Manan - Applied Sciences, 2023 - mdpi.com
The main purpose of this study is to investigate the thermal behavior of power law fluid
within a plus-shaped cavity under the influence of natural convection, also taking into …

A note on regularity criterion for 3D shear thickening fluids in terms of velocity

C Sin, ES Baranovskii - Mathematische Annalen, 2024 - Springer
We show that a weak solution for unsteady 3D shear thickening flows becomes a strong
solution, for 2≤ p< 11 5, provided that the velocity field u belongs to the critical space L β (0 …

Regularity criteria for 3D shear‐thinning fluids in terms of two components of vorticity

C Sin, J Pak, ES Baranovskii - Mathematical Methods in the …, 2023 - Wiley Online Library
In this paper, we show that a weak solution for unsteady flows of 3D shear‐thinning fluids is
strong under certain integrability assumptions about two components of the vorticity. In …

Regularity criterion for 3D shear-thinning fluids via one component of velocity

J Pak, C Sin, ES Baranovskii - Applied Mathematics & Optimization, 2023 - Springer
Regularity Criterion for 3D Shear-Thinning Fluids via One Component of Velocity | Applied
Mathematics & Optimization Skip to main content SpringerLink Account Menu Find a journal …

Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions

ES Baranovskii, OY Shishkina - Mathematics, 2024 - mdpi.com
In this paper, we investigate the solvability of a boundary value problem for a heat and mass
transfer model with the spatially averaged Rayleigh function. The considered model …

Boundary Value and Control Problems for the Stationary Magnetic Hydrodynamic Equations of Heat Conducting Fluid with Variable Coefficients

RV Brizitskii - Journal of Dynamical and Control Systems, 2024 - Springer
The global solvability and local uniqueness of boundary value problem's solutions for
stationary magnetic hydrodynamic equations for heat conducting fluid with variable …