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March  2005, 4(1): 23-43. doi: 10.3934/cpaa.2005.4.23

Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle

Colette Guillopé 1, , Abdelilah Hakim 2, and  Raafat Talhouk 3,

1. 

Laboratoire d'Analyse et de Mathématiques appliquées, CNRS et Université Paris XII -- Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
2. 

Mathématiques, Faculté des Sciences et Techniques de Guéliz, B.P. 549, Avenue Abdelkrim Elkhattabi, Marrakech, Morocco
3. 

Mathématiques, Faculté des Sciences Section 1, Université libanaise, Beyrouth, Lebanon

Received  April 2003 Revised  March 2004 Published  December 2004

This work is concerned with the study of steady flows, around an obstacle, of slightly compressible viscoelastic fluids, for which the extra-stress tensor is given by a White-Metzner constitutive law. The existence and uniqueness of such flows are shown, when Newtonian viscosity is present (Jeffreys' model), and for small data.
Keywords: Viscoelastic fluids, flows around obstacles., White-Metzner model, weak compressibility, steady flows.
Mathematics Subject Classification: 76D03, 35B10, 35B3.
Citation: Colette Guillopé, Abdelilah Hakim, Raafat Talhouk. Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle. Communications on Pure and Applied Analysis, 2005, 4 (1) : 23-43. doi: 10.3934/cpaa.2005.4.23
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