Model of a Nonuniformly Heated Viscous Flow through a Bounded Domain
- 1 March 2020
- journal article
- research article
- Published by Pleiades Publishing Ltd in Differential Equations
- Vol. 56 (3) , 304-314
Abstract
A mathematical model describing the flow of a nonuniformly heated viscous fluid through a bounded domain under slip boundary conditions is studied. Sufficient conditions are derived for the solvability of the problem in the class of weak solutions. Energy equalities for the solutions are obtained. It is shown that the set of weak solutions is sequentially weakly closed.Keywords
This publication has 9 references indexed in Scilit:
- The flux problem for the Navier-Stokes equationsRussian Mathematical Surveys, 2014
- Direct Methods in the Theory of Elliptic Equations2012
- Solvability of the stationary heat convection problem for a high-viscosity fluidDifferential Equations, 2009
- Topological Degree Theory and Applications2006
- On some unresolved issues in non-linear fluid dynamicsRussian Mathematical Surveys, 2003
- Unique Solvability of a Two-Dimensional Nonstationary Problem for the Convection Equations with Temperature-Dependent ViscosityDifferential Equations, 2002
- Solvability of stationary boundary control problems for heat convection equationsSiberian Mathematical Journal, 1998
- The Stokes and Navier-Stokes equations with boundary conditions involving the pressureJapanese Journal of Mathematics, 1994
- The problem of the flow of a non-uniformly heated viscous fluidUSSR Computational Mathematics and Mathematical Physics, 1989