Abstract
The linearized boundary-initial history value problem for simple fluids obeying the Coleman-Noll constitutive equation
is considered. Here S is the stress tensor, δ the Kronecker delta, p the constitutively indeterminate mean normal stress, E the infinitesimal strain tensor, and m(s) a material function. The shear relaxation modulus G is defined as
In this paper it is shown that if G satisfies the assumptions
then the rest state of the fluid is stable in an appropriate “fading memory” norm. The additional assumption
yields asymptotic stability.
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Slemrod, M. A hereditary partial differential equation with applications in the theory of simple fluids. Arch. Rational Mech. Anal. 62, 303–321 (1976). https://doi.org/10.1007/BF00248268
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DOI: https://doi.org/10.1007/BF00248268