Lieb-Thirring inequalities on the torus
Abstract
We consider the Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the γ-moments of the negative eigenvalues with constants independent of ratio of the periods. Applications to the attractors of the damped Navier-Stokes system are given.
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