\( H^m\) convergence of the second-grade fluid equations to Euler equations in \(\mathbb{R}^d\) (Q2187972)

Summary: In this paper, we investigate an approximation of the Euler equation by the second-grade fluid equations in \(\mathbb{R}^d\) (\( d = 2,3\)). The convergence in \(H^m\) of a sequence of solutions to the second-grade fluid equations in a uniform interval is proven as both the viscosity coefficient \(\left( \nu\right)\) and filter parameter \(\left( \alpha\right)\) tend to zero with an initial velocity in \(H^m\).