Abstract
Entropy methods have been widely used in the last years to obtain estimates of smoothness and asymptotic behavior for systems of PDEs, including kinetic equations, nonlinear diffusion equations, reaction-diffusion systems, higher-order equations, etc.
We present results recently obtained on the Landau equation. This equation models the collisions in plasmas due to the Coulomb interaction between charged particles. They are directly related to the study of the entropy production of the quadratic Landau operator, and to the Cercignani's conjecture of kinetic theory.
