Renormalized solutions for Boltzmann equation, Part II
Hamidreza Mahmoudian - Rutgers University
Location: Hill 703
Date & time: Wednesday, 17 October 2018 at 11:00AM - 12:30PM
Abstract: The Boltzmann equation describes the evolution of ideal gases, using a "correction" to the free transport equation as a result of molecular interactions. This correction is a second order integral operator, with a singularity in its definition (essentially because of infinite range molecular potentials) that makes the meaning of the equation unclear to begin with. To deal with the difficulties caused by nonlinearity, DiPerna and Lions introduced renormalized solutions. They, among other things, proved the first global existence result for a modified Boltzmann equation without the singularity. The first part of my talk will be a brief review of the equation and DiPerna-Lions theory, and in the second part I talk about some (relatively) new machinery devised by Villani et al. Their estimates allow an adaptation of renormalization techniques which is capable of dealing with the singular case.