# American Institute of Mathematical Sciences

October  2010, 14(3): 1001-1028. doi: 10.3934/dcdsb.2010.14.1001

## Regular flows of weakly compressible viscoelastic fluids and the incompressible limit

 1 Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France, France 2 Université Libanaise, Département de Mathématiques, Faculté de Sciences, Beyrouth, Lebanon

Received  September 2009 Revised  March 2010 Published  July 2010

We consider compressible viscoelastic fluids satisfying the Oldroyd constitutive law. We prove the local existence (and uniqueness) of flows by a classical fixed point argument. We also prove some global properties of the solutions. In particular, we obtain some a priori estimates which are uniform in the Mach number and prove global existence of weakly compressible fluids flows. We show that weakly compressible flows with well-prepared initial data converge to incompressible ones when the Mach number converges to zero.
Citation: Colette Guillopé, Zaynab Salloum, Raafat Talhouk. Regular flows of weakly compressible viscoelastic fluids and the incompressible limit. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1001-1028. doi: 10.3934/dcdsb.2010.14.1001
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