Local well‐posedness and zero‐ α  limit for the Euler‐ α  equations | Zendy

Yue Gaocheng | Zendy; Zhong Chengkui | Zendy

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Local well‐posedness and zero‐ α limit for the Euler‐ α equations

Author(s) -

Yue Gaocheng,

Zhong Chengkui

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4182

Subject(s) - inviscid flow , euler equations , mathematics , semi implicit euler method , zero (linguistics) , limit (mathematics) , backward euler method , euler method , mathematical analysis , regularization (linguistics) , euler's formula , rate of convergence , compressibility , convergence (economics) , classical mechanics , physics , linguistics , philosophy , channel (broadcasting) , artificial intelligence , economic growth , computer science , electrical engineering , economics , thermodynamics , engineering

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 inR 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 inR 2 . Copyright © 2016 John Wiley & Sons, Ltd.

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