Stopping a viscous fluid by a feedback dissipative field: Thermal effects without phase changing

Abstract

We show how the action on two simultaneous effects (a suitable coupling about velocity and temperature and a low range of temperature but upper that the phase changing one) may be responsible of stopping a viscous fluid without any changing phase. Our model involves a system, on an unbounded pipe, given by the planar stationary Navier-Stokes equation perturbed with a sublinear term f(x,θ, u) coupled with a stationary (and possibly nonlinear) advection diffusion equation for the temperature θ. After proving some results on the existence and uniqueness of weak solutions we apply an energy method to show that the velocity u vanishes for x large enough.