Seminar Analysis and Mathematical Physics: Dr. Raphael Winter (ENS Lyon)

Rigorous validity of the Choh-Uhlenbeck equation

Following the pioneering work of Lanford, a rigorous theory has been developed for the validation of the Boltzmann equation in the low-density Grad scaling. In the physics literature, an important issue are the corrections to the equation for small but positive volume fraction. The first order correction to the Boltzmann equation is conjectured to be given by the so-called Choh-Uhlenbeck equation, which is of the form

∂tfϵ=Qϵ,BE(fϵ,fϵ)+ϵQϵ,CU(fϵ,fϵ,fϵ).

Here Qϵ,BE is the Boltzmann-Enskog operator, and the Choh-Uhlenbeck operator Qϵ,CU is an explicit cubic operator. This operator accounts for the formation of dynamic microscopic correlations between three particles. In this work, we prove rigorously that the Choh-Uhlenbeck equation gives the first order correction to the Boltzmann equation in the Grad-scaling. This is a joint work with Sergio Simonella.

Veranstaltung übernehmen als iCal