Energy criterion of nonlinear stability of a flow of the Rivlin–Ericksen fluid in porous medium

Abstract

Nonlinear stability of the motionless state of the thermosolutal Rivlin–Ericksen fluid in porous medium for the case of stress-free boundaries is studied by generalized energy method. By means of introducing an energy functional we will prove a sufficient condition for unconditional nonlinear stability of the motionless state. The nonlinearly stabilizing effect of concentration on the system is proved. Furthermore, for certain range of system parameters our sufficient condition for stability is also necessary.