2015/07/04 by Jing Tian, Bingsheng Zhang, Tian, Jing +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1507.01142
openalex publication_date 2015/07/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is not yet known if the global attractor of the space periodic 2D Navier-Stokes equations contains nonstationary solutions u(x,t) such that their energy and enstrophy per unit mass are constant for every t ∈ (-∞, ∞). The study of the properties of such solutions was initiated in \citeCMM13, where, due to the hypothetical existence of such solutions, they were called "ghost solutions". In this work, we introduce and study geometric structures shared by all ghost solutions. This study led us to consider a subclass of ghost solutions for which those geometric structures have a supplementary stability property. In particular, we show that the wave vectors of the active modes of this subclass of ghost solutions must satisfy certain supplementary constraints. We also found a computational way to check for the existence of these ghost solutions.