Uniform time of existence for the alpha Euler equations
Uniform time of existence for the alpha Euler equations
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DOI：
10.1016/j.jfa.2016.06.006
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
A. Busuioc;D. Iftimie;M. L. Filho;H. N. Lopes
中科院分区：
文献类型：
--
作者：
A. Busuioc;D. Iftimie;M. L. Filho;H. N. Lopes
考虑具有无摩擦Navier边界条件的有界三维区域上的α-欧拉方程。我们的主要结果是，对于足够小的α，在正时间区间上存在一个强解，且在α中是一致的。结合[6]的收敛结果，表明α-欧拉方程的解在α→0时收敛于不可压缩欧拉方程的解。此外，我们还得到了三维有界区域上不可压缩欧拉方程强解的局部存在性的一个新结果。这些证明是基于在正态空间中的新的先验估计。
We consider the α-Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in α, for α sufficiently small. Combined with the convergence result in [6], this implies convergence of solutions of the α-Euler equations to solutions of the incompressible Euler equations when α→ 0. In addition, we obtain a new result on local existence of strong solutions for the incompressible Euler equations on bounded three-dimensional domains. The proofs are based on new a priori estimates in conormal spaces.