Semigroup decay for the linearized kinetic ellipsoidal Fokker-Planck equation

In this paper, we deal with the semigroup decay for the linearized kinetic ellipsoidal Fokker-Planck equation in the torus. This model is an extension of the nonlinear kinetic Fokker-Planck equation in order to give a correct Prandtl number in the Navier-Stokes limit. Due to the diffusion coefficient is replaced by a non diagonal temperature tensor, this makes the linearized operator for the nonlinear kinetic ellipsoidal Fokker-Planck equation with more complicated form. By taking advantage of the H-1 type hypocoercivity techniques, we prove that the solutions converge exponential to the equilibrium with explicit rates. (c) 2022 Elsevier Inc. All rights reserved.