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arXiv · 1804.09632

Lieb--Thirring inequalities on the sphere

Alexei Ilyin·Ari Laptev
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Abstract

We prove on the sphere $\mathbb{S}^2$ the Lieb--Thirring inequalities 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 we obtain an explicit estimate for the dimension of the attractor of the Navier--Stokes system on a domain on the sphere with Dirichlet non-slip boundary conditions.

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Alexei Ilyin, Ari Laptev. 2018-04-25. Lieb--Thirring inequalities on the sphere. https://arxiv.org/abs/1804.09632

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