On second grade fluids with vanishing viscosity |
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Institution: | 1. Humboldt-Universität zu Berlin, Berlin, Germany;2. Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany |
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Abstract: | We consider in ℝn (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. |
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