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Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models. (English) Zbl 1302.76009
Summary: We prove exponential asymptotic stability for the corotational incompressible diffusive Johnson-Segalman viscolelastic model and a simple decay result for the corotational incompressible hyperbolic Maxwell model. Moreover we establish continuous dependence and uniqueness results for the non-zero equilibrium solution.
In the compressible case, we prove a Hölder continuous dependence theorem upon the initial data and body force for both models, whence follows a result of continuous dependence on the initial data and, therefore, uniqueness.
For the Johnson-Segalman model we have also dealt with the case of negative elastic viscosities, corresponding to retardation effects. A comparison with other type of viscoelasticity, showing short memory elastic effects, is given.

MSC:
76A05 Non-Newtonian fluids
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
76A10 Viscoelastic fluids
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