Decay of the kinetic and the thermal energy of incompressible micropolar fluids

ABSTRAcr. We consider a heat conducting incompressible micropolar fluid at rest and filling a closed rigid container. We account for the heat generated due to viscous dissipation and show that the kinetic and the thermal energy of arbitrary disturbances of the rest state decays exponentially. The rate of decay depends upon the viscosity coefficients, heat conduction coefficients and the size and shape of the container.