Qi Wang

Department of Mathematics

Indiana University-Purdue University

**Abstract:**
The stability of the rest state of a Newtonian fluid subjected to small
perturbations is examined. For unconstrained materials the rest state is
found to be stable but when the density of the fluid is constrained to be
a function of temperature along the rest state becomes unstable. We
suggest a possible remedy for this situation, considering density to be
a function of the specific entropy. We consider these constrained
situations as limits of the unconstrained case and show the connection
between the two types of constraints.