On Solutions of the 2D Navier-Stokes Equations with Constant Energy and Enstrophy Jing TianBo Zhang 35Q3035B4175D05Navier-Stokes equationsglobal attractorenergyenstrophy It is not yet known if the global attractor of the space-periodic 2D Navier-Stokes equations contains non-stationary solutions $u(x,t)$ such that their energy and enstrophy per unit mass are constant for every $\in(-\infty,\infty)$. The study of the properties of such solutions was initiated in \cite{CMM13}, where, because of 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 leads 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 discover a computational way to check for the existence of these ghost solutions. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5725 10.1512/iumj.2015.64.5725 en Indiana Univ. Math. J. 64 (2015) 1925 - 1958 state-of-the-art mathematics http://iumj.org/access/