This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations. The author's analysis of these equations concentrates on thermal convection in a layer of incompressible fluid. Readers will learn how the Navier-Stokes equations, the Kelvin-Voigt equations, and the Navier-Stokes-Voigt equations are special cases of the generalized Oskolkov system. Thermal convection and double-diffusive convection are studied in Navier-Stokes-Voigt fluids and in various Kelvin-Voigt and Oskolkov fluids. Cutting edge research is included on magnetohydrodynamic convection in a Navier-Stokes-Voigt fluid and in a Kelvin-Voigt fluid of order one.

Oskolkov Equations and Thermal Convection will serve as a timely resource for students and researchers interested in this active topic, as well as those studying the broader area of fluid dynamics.

Autorentext

Brian Straughan's research is in partial differential equations, scientific computing, and their applications to problems in the real world.

Inhalt

Introduction.- The Navier-Stokes Equations.- Navier-Stokes-Voigt Equations.- Navier-Stokes-Voigt Equations, further problems.- Kelvin-Voigt Equations.- Oskolkov Equations.- Magnetohydrodynamic Convection.- Oskolkov Equations in Porous Media.- Further Developments in Porous Media Equations.