BooksStandalone TitlesCollected Volumepp. 583–608

Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamics

  • Alexei Ilyin

    Keldysh Institute of Applied Mathematics, Moscow, Russia; Sirius University of Science and Technology, Sochi, Russia
  • Anna Kostianko

    Imperial College London, United Kingdom
  • Sergey Zelik

    University of Surrey, Guildford, UK; Lanzhou University, China, Keldysh Institute of Applied Mathematics, Moscow, Russia
Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamics cover
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Abstract

We discuss the estimates for the Lp{L^{p}}-norms of systems of functions that are orthonormal in L2{L^{2}} and H1{H^{1}}, 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 α{\alpha}-models approximating them. New applications to interpolation inequalities on the two-dimensional torus are also given.