Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions

Abstract

In this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3). On the other hand, the relationship between the Hs{H}^{s}-norm of the velocity field and the parameter α\alpha is clarified.

Keywords

• non-newtonian fluids
• well-posedness for pdes
• euler-α equations
• euler equations
• 35a01
• 35d35
• 35q35