Abstract
We consider the equations of a linear Maxwell fluid with spatially varying coefficients. Pure stress modes are solutions with zero velocity but nonzero stresses. We derive equations to characterize such solutions. In two dimensions, we find that under generic hypotheses only certain “trivial” solutions exist. In three dimensions, on the other hand, there exist nontrivial solutions. To get them, we derive a system of partial differential equations whose type (elliptic or hyperbolic) depends on the sign of the Gauss curvature of level surfaces of the relaxation time.
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The research of Debanjana Mitra and Michael Renardy was supported by the National Science Foundation under Grant DMS-1514576. Mythily Ramaswamy was supported in part by a Fulbright-Nehru Academic and Professional Excellence Fellowship.
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Mitra, D., Ramaswamy, M. & Renardy, M. Pure stress modes for linear viscoelastic flows with variable coefficients. Z. Angew. Math. Phys. 70, 97 (2019). https://doi.org/10.1007/s00033-019-1140-0
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DOI: https://doi.org/10.1007/s00033-019-1140-0