References
Coleman, B. D., & W. Noll, An approximation theorem for functionals with applications in continuum mechanics. Arch. Rational Mech. Anal. 6, 355–370 (1960).
Coleman, B. D., & W. Noll, Foundations of linear viscoelasticity. Rev. Modern Phys. 33, 239 (1961). Erratum. 36, 1103 (1964).
Coleman, B. D., & H. Markovitz. Normal stress effects in second-order fluids. J. App. Phys. 35, 1 (1964).
Coleman, B. D., R. J. Duffin & V. J. Mizel, Instability, uniqueness and nonexistence theorems for the equation U t =U xx U xtx on a strip. Arch. Rational Mech. Anal. 19, 100–116 (1965).
Coleman, B. B., & V. Mizel, Breakdown of laminar shearing flows for second-order fluids in channels of critical width. ZAMM 46, 445–448 (1966).
Craik, A. D., A note on the static stability of an elastoviscous fluids. J. Fluid Mech. 33, 33–39 (1968).
Green, A. E., & R. Rivlin, The mechanics of non-linear materials with memory. Part 1. Arch. Rational Mech. Anal. 1, I (1957).
Joseph, D. D., Slow motion and viscometric motion; stability and bifurication of the rest state of a simple fluid. Arch. Rational Mech. Anal. 56, 99–157 (1974).
Joseph, D. D., Some inequalities in the theory of simple fluids. Rheologica Acta 19, 299–300 (1980).
Joseph, D. D., Stability of Fluid Motions. Chap. XIII, Vol. II, Berlin-Heidelberg-New York: Springer Tracts in Natural Philosophy, 1976.
Joseph, D. D., & G. S. Beavers, Free surface problems in rheological fluid mechanics. Rheologica Acta 16 (1977).
Slemrod, M., A hereditary partial differential equation with applications in the theory of simple fluids. Arch. Rational Mech. Anal. 62, 303–322 (1976).
Author information
Authors and Affiliations
Additional information
This paper was supported by the U.S. Army Research Office and the NSF.
Rights and permissions
About this article
Cite this article
Joseph, D.D. Instability of the rest state of fluids of arbitrary grade greater than one. Arch. Rational Mech. Anal. 75, 251–256 (1981). https://doi.org/10.1007/BF00250784
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00250784