On coupled system of Navier-Stokes equations and temperature in infinite channel

Abstract

This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier-Stokes equations in a strip in such spaces has been established in Zelik (2007). Similar protocol is observed using maximum principle to obtain bounds for the temperature solutions in Boussinesq approximation.

Keywords: Naviernavier-Stokes Equations, Unbounded Domains, Infinite-Energy Solutions, Uniformly Local Spaces, Boussinesq Approximation, Maximum Principle