Controllability of viscoelastic stresses for nonlinear Maxwell models |
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| Authors: | Michael Renardy |
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| Institution: | 1. Departamento de Matemática Aplicada I, Universidade de Vigo Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain;2. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela Escola Politécnica Superior, Campus Universitario, 27002 Lugo, Spain;1. Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349 Besiktas, Istanbul, Turkey;2. Inst. of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 370141 Baku, Azerbaijan;3. Yildiz Technical University, Faculty of Civil Engineering, Department of Civil Engineering, Davutpasa Campus, 34220 Esenler, Istanbul, Turkey;4. Turgut Ozal University, Faculty of Engineering, Department of Civil Engineering, 06010 Kecioren, Ankara, Turkey;1. Department of Materials Science and Engineering, National Cheng Kung University, Tainan, Taiwan;2. Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, Taiwan;1. Centre de Recherche de Solaize (CReS), Total Marketing Services, Solaize, France;2. Univ Lyon, INSA-Lyon, CNRS, LaMCoS, UMR5259, F-69621, Villeurbanne, France;1. Department of Mathematics, University of Craiova, Craiova, 200585, Romania;2. Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy (ISMMA), Bucharest, 050711, Romania;3. Inria, SPHINX, Villers-lès-Nancy, F-54600, France;4. Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, CNRS, 54506 Vand?uvre-lès-Nancy Cedex, France |
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| Abstract: | We investigate a class of models for viscoelastic fluids, in which the elastic stress is determined by a conformation tensor, and the conformation tensor is linked to the velocity field by a system of ordinary differential equations. We study the question which values of the conformation tensor can be reached in a homogeneous flow, subject to a given initial condition and arbitrary velocity fields. This problem is a special “easy” case for the question of controllability of viscoelastic flows. For a class of models, we show that constraints on the values of the conformation tensor are given by lower and/or upper bounds on its determinant. The behavior of seemingly similar models, e.g. the PTT, Giesekus and Peterlin dumbbell models, turns out to be surprisingly different. |
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