Lieb–Thirring inequalities on the sphere

Ilyin, A.; Laptev, A.

doi:10.1090/spmj/1609

Lieb–Thirring inequalities on the sphere
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by A. Ilyin and A. Laptev

St. Petersburg Math. J. 31 (2020), 479-493

DOI: https://doi.org/10.1090/spmj/1609

Published electronically: April 30, 2020

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Abstract:

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.

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