On a Subclass of Solutions of the 2D Navier–Stokes Equations with Constant Energy and Enstrophy
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In this paper, we are interested in studying the existence of the nonstationary solutions in the global attractor of the 2D Navier–Stokes equations with constant energy and enstrophy. We particularly focus on a subclass of these solutions that the geometric structures have a supplementary stability property which were called “chained ghost solutions” in Tian and Zhang (Indiana Univ Math J 64:1925–1958, 2015). By solving a Galerkin system of a particular form, we show the nonexistence of the chained ghost solutions for certain cases.
Keywords2D Navier–Stokes equations Chained ghost solution Energy Enstrophy
Mathematics Subject Classification35Q30 35B41 76D05
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