On some global solutions to 3d incompressible heat-conducting motions
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.