Special Session 17: Nonlinear models in kinetic theory, collective behavior, and fluid dynamics

Continuity for Nonlocal Hypoelliptic Kinetic Equations

Logan Stokols
Duke University
USA
Co-Author(s):    
Abstract:
In this talk, we`ll explore a family of nonlocal kinetic equations that generalize the well-known Fokker-Planck equation and linearize the non-cutoff Boltzmann equation. We use a combination of hypoelliptic properties and De Giorgi`s method to obtain H\{o}lder continuity. Since our approach is entirely energy based, we can account for unbounded source terms and a wide range of dissipative degrees.