Local well‐posedness and zero‐α limit for the Euler‐α equations. (15th September 2016)

• Record Type: Journal Article
• Authors: Yue, Gaocheng; Zhong, Chengkui
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 7(2017)
• Page Start: 2566
• Page End: 2581
• Publication Date: 2016-09-15
• Subjects: Euler‐α equations -- Littlewood–Paley theory -- blow‐up criterion; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4182
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we prove the local‐in‐time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler‐ α equations of inviscid incompressible fluid flows in R d, d ≥ 2 . We also establish the convergence rate of the solutions of the Euler‐ α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 in R 2 . Copyright © 2016 John Wiley & Sons, Ltd.