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REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693010
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Submitted on : Tuesday, May 1, 2012 - 7:28:23 PM
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Colette Guillope, Zaynab Salloum, Raafat Talhouk. REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2010, 14 (3), pp.1001--1028. ⟨10.3934/dcdsb.2010.14.1001⟩. ⟨hal-00693010⟩

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