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arXiv · 2202.01531

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

Alexei Ilyin·Anna Kostianko·Sergey Zelik
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Abstract

We discuss the estimates for the $L^p$-norms of systems of functions that are orthonormal in $L^2$ and $H^1$, 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 $\alpha$-models approximating them. New applications to interpolation inequalities on the 2D torus are also given.

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Alexei Ilyin, Anna Kostianko, Sergey Zelik. 2022-02-03. Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics. https://arxiv.org/abs/2202.01531

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