LIEB-THIRRING INEQUALITIES ON THE SPHERE

摘要

On the sphere 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 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.