Newtonian limit for weakly viscoelastic fluid flows of Olroyds' type

dc.creatorMolinet, Luc
dc.creatorTalhouk, Raafat
dc.date2008-03-03
dc.date.accessioned2026-07-07T09:24:21Z
dc.date.available2026-07-07T09:24:21Z
dc.descriptionThis paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for $N=2, 3$, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field and the extra-stress tensor converge in their existence spaces (we examine the Sobolev-$H^s$ theory and the Besov-$B^{s,1}_2$ theory to reach the critical case $s= N/2$) to the corresponding newtonian quantities. These convergence results are established in the case of "ill-prepared"' data.We deduce, in the two-dimensional case, a new result concerning the global existence of weakly viscoelastic fluids flow. Our approach makes use of essentially two ingredients : the stability of the null solution of the viscoelastic fluids flow and the damping effect,on the difference between the extra-stress tensor and the tensor of rate of deformation, induced by the constitutive law of the fluid.
dc.identifierhttps://arxiv.org/abs/0803.0228
dc.identifierhttp://arxiv.org/abs/0803.0228
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156064
dc.subjectAnalysis of PDEs
dc.subject76D03; 35B05
dc.titleNewtonian limit for weakly viscoelastic fluid flows of Olroyds' type
dc.typetext

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