An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid

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• 作者：Yoshitaka Watanabe ; ^{watanabe@cc.kyushu-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：35Q30 ; 65N15 ; 76D03
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：157-170
• 全文大小：2310 K

文摘

Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009).