Illposedness in a Thermomechanically Consistent Constrained Theory for Materials with Prescribed Temperature-dependent Density
نویسنده
چکیده
We examine the local dynamics of nonisothermal viscous ows 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. (1996). We discover that the linearized growth rate of small length scale, innnitesimal disturbances near the equilibria is proportional to the reciprocal of their wave length, a classical phenomenon known as the Hadamard instability, indicating the local illposed-ness of the constrained theory. Therefore, the use of the theory to model transient ow phenomenon is not advised.
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