Global Well-Posedness of 2D Second Grade Fluid Equations in Exterior Domain

Abstract

In this article, we consider 2D second grade fluid equations in exterior domain with Dirichlet boundary conditions. For initial data ${\mathbf{u}}_0\in {\mathbf{H}}^3(\Omega )$, the system is shown to be global well-posed. Furthermore, for arbitrary $T>0$ and $s\ge 3$, we prove that the solution belongs to $L^{\infty }([0,T];{\mathbf{H}}^s(\Omega ))$ provided that ${\mathbf{u}}_0$ is in ${\mathbf{H}}^s(\Omega )$.

References in corpus (2)

• Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions
• Global Well-Posedness of 2D Euler-$\alpha$ Equations in Exterior Domain

Cited by in corpus (1)

• Singular limit of 2D second grade fluid past an obstacle