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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Lieb–Thirring inequalities on the sphere

Authors: A. Ilyin and A. Laptev
Original publication: Algebra i Analiz, tom 31 (2019), nomer 3.
Journal: St. Petersburg Math. J. 31 (2020), 479-493
MSC (2010): Primary 35P15, 26D10, 35Q30.
Published electronically: April 30, 2020
MathSciNet review: 3985921
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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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Additional Information

A. Ilyin
Affiliation: Keldysh Institute of Applied Mathematics

A. Laptev
Affiliation: Imperial College London; Institute Mittag–Leffler

Keywords: Lieb–Thirring inequalities, spectral inequalities on the sphere, Navier–Stokes equations, attractors
Received by editor(s): April 29, 2018
Published electronically: April 30, 2020
Additional Notes: A. L. was partially supported by the Russian Science Foundation grant 19-71-30002
Dedicated: Dedicated to the memory of S. G. Mikhlin
Article copyright: © Copyright 2020 American Mathematical Society