arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 1902.00384math.APphysics.flu-dyn
收藏

Navier-Stokes流中的自发周期轨道

Spontaneous periodic orbits in the Navier-Stokes flow

Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard, Lennaert van Veen

摘要:

本文提出了一种构造性证明三环面上受迫自治Navier-斯托克斯方程周期轨道存在性的一般方法。在引入几何衰减的傅里叶系数的巴拿赫空间上的一个零点寻找问题后,应用Newton-Kantorovich定理得到了存在性的(计算机辅助)证明.所需的分析估计,以验证该运营商的可收缩性提出了充分的一般性和对称性的模型被用来减少要解决的问题的大小。作为应用,我们证明了具有Taylor-Green强迫的Navier-斯托克斯方程的自发周期轨道的存在性.

英文摘要:

In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier-Stokes equations on the three-torus is proposed. After introducing a zero finding problem posed on a Banach space of geometrically decaying Fourier coefficients, a Newton-Kantorovich theorem is applied to obtain the (computer-assisted) proofs of existence. The required analytic estimates to verify the contractibility of the operator are presented in full generality and symmetries from the model are used to reduce the size of the problem to be solved. As applications, we present proofs of existence of spontaneous periodic orbits in the Navier-Stokes equations with Taylor-Green forcing.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑