The uniform time of existence of the smooth solution for 3D Euler-α equations with Dirichlet boundary conditions

2016/04/14 by Aibin Zang, Zang, Aibin
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1604.04083

openalex publication_date 2016/04/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

After reformulate the incompressible Euler-α equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-α equations exist in uniform time interval independent of α. We also show the solution of the Euler-α converge to the corresponding solution of Euler equation in L² in space, uniformly in time. In the sequel, it follows that the H^s (s>(n)/(2)+1) solutions of Euler-α equations exist in any fixed sub-interval of the maximum existent interval for the Euler equations provided that initial is regular enough and α is small sufficiently.

Related

• Uniform time of existence for the alpha Euler equations
• Construction of solutions to the 3D Euler equations with initial data in H^β for β>0
• Non-conservative H^{\frac 12-} weak solutions of the incompressible 3D Euler equations
• Non-conservative solutions of the Euler-α equations
• Finite-Time Singularity Formation for C^1,α Solutions to the Incompressible Euler Equations on ℝ³