Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamics
Alexei IlyinKeldysh Institute of Applied Mathematics, Moscow, Russia; Sirius University of Science and Technology, Sochi, Russia
Anna KostiankoImperial College London, United Kingdom
Sergey ZelikUniversity of Surrey, Guildford, UK; Lanzhou University, China, Keldysh Institute of Applied Mathematics, Moscow, Russia
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We discuss the estimates for the -norms of systems of functions that are orthonormal in and , respectively, and their essential role in deriving good or even optimal bounds for the dimension of global attractors for the classical Navier–Stokes equations and for a class of -models approximating them. New applications to interpolation inequalities on the two-dimensional torus are also given.