Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 59, No. 1, pp. 47-65 (2002)

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On Second Grade Fluids with Vanishing Viscosity

Valentina Busuioc

Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, BC 187,
175, rue Chevaleret, 75252 Paris -- FRANCE
E-mail: busuioc@ann.jussieu.fr

Abstract: We consider the equation of a second grade fluid with vanishing viscosity, also known as Camassa--Holm equation, and we prove local existence and uniqueness of solutions for smooth initial data. We also give a blow-up condition which implies that the solution is global in dimension 2. Finally, we prove the convergence of the solutions of second grade fluid equation to the solution of the Camassa--Holm equation as the viscosity tends to zero.

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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