Ill-Posedness in a Thermomechanically Consistent Constrained Theory for Materials With Prescribed Temperature-Dependent Density

Abstract

We examine the local dynamics of nonisothermal viscous flows in the neighborhood of the constant equilibria using the thermomechanically consistent constrained theory for materials with prescribed temperature-dependent density developed by Cao et al.. We discover that the linearized growth rate of small length scale, infinitesimal disturbances near the equilibria is proportional to the reciprocal of their wave length, a classical phenomenon known as the Hadamard instability, indicating the local ill-posedness of the constrained theory. Therefore, the use of the theory to model transient flow phenomenon is not advised. [S0021-8936(00)01901-2]