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Local well‐posedness and zero‐α limit for the Euler‐α equations
Authors:Gaocheng Yue  Chengkui Zhong
Affiliation:1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China;2. Department of Mathematics, Nanjing University, Nanjing, China
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 urn:x-wiley:mma:media:mma4182:mma4182-math-0001. 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 urn:x-wiley:mma:media:mma4182:mma4182-math-0002. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:Euler‐α   equations  Littlewood–  Paley theory  blow‐up criterion
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