Abstract
In this paper we have proved 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 have established continuous dependence and uniqueness results for the non-zero equilibrium solution.   In the compressible case, we have proved 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.
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