Global Hypoellipticity and Compact Resolvent for Fokker-Planck Operator

Gyrokinetic Fokker-Planck Collision Operator

Gyrokinetic Fokker-Planck Collision Operator

Gyrokinetic Fokker-Planck collision operator.

The gyrokinetic linearized exact Fokker-Planck collision operator is obtained in a form suitable for plasma gyrokinetic equations, for arbitrary mass ratio. The linearized Fokker-Planck operator includes both the test-particle and field-particle contributions, and automatically conserves particles, momentum, and energy, while ensuring non-negative entropy production. Finite gyroradius effects i...

Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential

We consider the Fokker-Planck equation with a confining or anti-confining potential which behaves at infinity like a possibly high degree homogeneous function. Hypoellipticity techniques provide the well-posedness of the weakCauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium. Lower and upper bounds for the rate of convergence to equilibrium are ...

The Gevrey Hypoellipticity for Linear and Non-linear Fokker-planck Equations

Recently, a lot of progress has been made on the study for the spatially homogeneous Boltzmann equation without angular cutoff, cf. [2, 3, 8, 22] and references therein, which shows that the singularity of collision cross-section yields some gain of regularity in the Sobolev space frame on weak solutions for Cauchy problem. That means, this gives the C regularity of weak solution for the spatia...