Lieb-Thirring inequalities on the sphere

A. Ilyin ; A. Laptev

Algebra i analiz, Tome 31 (2019) no. 3, pp. 116-135.

Résumé

On the sphere $ \mathbb{S}^2$, the Lieb-Thirring inequalities are proved for orthonormal families of scalar and vector functions both on the whole sphere and on proper domains on $ \mathbb{S}^2$. By way of applications, an explicit estimate is found for the dimension of the attractor of the Navier-Stokes system on a domain on the sphere with Dirichlet nonslip boundary conditions.

Détail

Keywords: Lieb–Thirring inequalities, spectral inequalities on the sphere, Navier–Stokes equations, attractors.

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