On second-grade fluids with vanishing viscosity
Summary: 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 two. Finally, we prove the convergence of solutions of second-grade fluid equation to the solution of Camassa-Holm equation as the viscosity tends to zero.
scientific article; zbMATH DE number 1787282
scientific article