Abstract:
We consider the Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the γ-moments of the negative eigenvalues with constants independent of ratio of the periods. Applications to the attractors of the damped Navier-Stokes system are given.
Bibliography: 33 titles.
\Bibitem{IlyLap16}
\by A.~A.~Ilyin, A.~A.~Laptev
\paper Lieb-Thirring inequalities on the torus
\jour Sb. Math.
\yr 2016
\vol 207
\issue 10
\pages 1410--1434
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https://www.mathnet.ru/eng/sm8641
https://doi.org/10.1070/SM8641
https://www.mathnet.ru/eng/sm/v207/i10/p56
This publication is cited in the following 8 articles:
Alexei Ilyin, Ari Laptev, Timon Weinmann, “Lieb–Thirring Inequalities on Manifolds with Constant Negative Curvature”, J Geom Anal, 34:2 (2024)
André Kowacs, Michael Ruzhansky, “Lieb–Thirring inequalities on the spheres and SO(3)”, Anal.Math.Phys., 14:6 (2024)
Advances in Mathematics, 412 (2023), 108815
J. Math. Phys., 63:4 (2022), 043503
A. Ilyin, A. Laptev, S. Zelik, “Lieb-thirring Constant on the Sphere and on the Torus”, J. Funct. Anal., 279:12 (2020), 108784
St. Petersburg Math. J., 31:3 (2020), 479–493
S. V. Zelik, A. A. Ilyin, A. A. Laptev, “On the Lieb–Thirring Constant on the Torus”, Math. Notes, 106:6 (2019), 1020–1024
V. Chepyzhov, A. Ilyin, S. Zelik, “Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions”, Phys. D, 376 (2018), 31–38
Citation in format AMSBIB
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