Abstract
We prove an existence and uniqueness theorem for three-dimensional motions of a certain class of simple, incompressible materials. The constitutive equation is assumed to have, in addition to a Newtonian part, a viscoelastic part given by a smooth, bounded functional of the history of the displacement gradient. Both displacement and traction boundary conditions are considered.
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Communicated by D. D. Joseph
This study was sponsored by the Deutsche Forschungsgemeinschaft and was supported in part by the U.S. Army Research Station, Durham.
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Renardy, M. Local existence theorems for the first and second initial-boundary value problems for a weakly non-newtonian fluid. Arch. Rational Mech. Anal. 83, 229–244 (1983). https://doi.org/10.1007/BF00251510
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DOI: https://doi.org/10.1007/BF00251510