On some global solutions to 3d incompressible heat-conducting motions
Volume 119 / 2017
Annales Polonici Mathematici 119 (2017), 79-94
MSC: Primary 35B35; Secondary 35Q30, 76D05, 80A20.
DOI: 10.4064/ap4048-2-2017
Published online: 20 March 2017
Abstract
We consider stability of solutions to stationary Navier–Stokes equations coupled with the heat equation in a set of solutions to the corresponding nonstationary system. The coupling is such that in the right-hand side of the Navier–Stokes equations there is a power function of temperature and in the equation for temperature there is a viscous dissipation term. We consider the non-slip boundary condition for velocity and the Dirichlet boundary condition for temperature. Moreover, the existence of a global strong-weak solution which remains close to the stationary solution for all time is proved.
