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Partial Differential Equations Seminar

Tuesday, November 3, 2020 - 12:15pm

Sanchit Chaturvedi

Stanford University

Location

University of Pennsylvania

seminar will be at Zoom link

The vector field method developed by Klainerman has been widely successful in the study of wave equations and general relativity. Recently, the vector field approach has been adapted to understand the dispersion due to the transport operator in both collisionless and collisional kinetic models. As an application of the approach, I will briefly discuss the stability of vacuum for Landau equation results (due to Luk for the moderately soft potentials case and due to me for the hard potentials case). Next, I will discuss my recent result on stability of vacuum for Boltzmann equation with moderately soft potentials. 
In addition to understanding dispersion, the vector field approach can be used to understand phase mixing in the weakly collisional regime. To illustrate that I will present a work in progress (in collaboration with Jonathan Luk and Toan Nguyen) where we consider the Vlasov--Poisson--Landau equation in the weakly collisional regime and prove that the for appropriately small sized data, the solution exhibits enhanced dissipation and Landau damping.

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