`a`
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models

Pages: 2111 - 2132, Volume 19, Issue 7, September 2014      doi:10.3934/dcdsb.2014.19.2111

 
       Abstract        References        Full Text (427.5K)       Related Articles       

Franca Franchi - Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy (email)
Barbara Lazzari - Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy (email)
Roberta Nibbi - Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy (email)

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.

Keywords:  Johnson-Segalman viscolestic fluids, Maxwell viscoelastic fluids, continuous dependence, stability, relaxation/retardation effects.
Mathematics Subject Classification:  Primary: 76A05, 35B30; Secondary: 76A10.

Received: April 2013;      Revised: July 2013;      Available Online: August 2014.

 References