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On second grade fluids with vanishing viscosity. (English. Abridged French version) Zbl 0935.76004

Summary: We consider in \(\mathbb{R}^n\) \((n= 2,3)\) the equation of a second grade fluid with vanishing viscosity, also known as Camassa-Holm equation. 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 for \(n=2\). 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.

MSC:

76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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