REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT

Colette Guillope (1) , Zaynab Salloum (1) , Raafat Talhouk

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Physique mathématique [math-ph]

Colette Guillope, Zaynab Salloum, Raafat Talhouk. REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT. Discrete and Continuous Dynamical Systems - Series B, 2010, 14 (3), pp.1001--1028. ⟨10.3934/dcdsb.2010.14.1001⟩. ⟨hal-00693010⟩