Busuioc, Valentina On second grade fluids with vanishing viscosity. (English. Abridged French version) Zbl 0935.76004 C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 12, 1241-1246 (1999). 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. Cited in 38 Documents MSC: 76A05 Non-Newtonian fluids 35Q35 PDEs in connection with fluid mechanics Keywords:Camassa-Holm equation; local existence; uniqueness; smooth initial data; blow-up condition; convergence PDFBibTeX XMLCite \textit{V. Busuioc}, C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 12, 1241--1246 (1999; Zbl 0935.76004) Full Text: DOI