29 research outputs found
Lieb-Thirring inequalities on some manifolds
We prove Lieb-Thirring inequalities with improved constants on the
two-dimensional sphere and the two-dimensional torus. In the one-dimensional
periodic case we obtain a simultaneous bound for the negative trace and the
number of negative eigenvalues
Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations
We derive upper bounds for the number of asymptotic degrees (determining
modes and nodes) of freedom for the two-dimensional Navier--Stokes system and
Navier-Stokes system with damping. In the first case we obtain the previously
known estimates in an explicit form, which are larger than the fractal
dimension of the global attractor. However, for the Navier--Stokes system with
damping our estimates for the number of the determining modes and nodes are
comparable to the sharp estimates for the fractal dimension of the global
attractor. Our investigation of the damped-driven 2D Navier--Stokes system is
inspired by the Stommel--Charney barotropic model of ocean circulation where
the damping represents the Rayleigh friction. We remark that our results
equally apply to the Stommel--Charney model
On the Domain of Analyticity and Small Scales for the Solutions of the Damped-driven 2D Navier-Stokes Equations
We obtain a logarithmically sharp estimate for the space-analyticity radius
of the solutions of the damped-driven 2D Navier-Stokes equations with periodic
boundary conditions and relate this to the small scales in this system. This
system is inspired by the Stommel--Charney barotropic ocean circulation model
One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrodinger operators
In this paper we prove refined first-order interpolation inequalities for
periodic functions and give applications to various refinements of the
Carlson--Landau-type inequalities and to magnetic Schrodinger operators. We
also obtain Lieb-Thirring inequalities for magnetic Schrodinger operators on
multi-dimensional cylinders.Comment: 33