Apr 12 2021

Analysis and Applied Mathematics Seminar: Hardy inequalities for the Landau equation, by Maria Pia Gualdani

April 12, 2021

4:00 PM - 4:50 PM

Location

Zoom

Address

Chicago, IL

Maria Pia Gualdani (UT Austin): Hardy inequalities for the Landau equation

Kinetic equations are used to describe evolution of interacting particles. The most famous kinetic equation is the Boltzmann equation: formulated by Ludwig Boltzmann in 1872, this equation describes motion of a large class of gases. Later, in 1936, Lev Landau derived a new mathematical model for motion of plasma. This latter equation was named the Landau equation. One of the main features of the Landau equation is nonlocality, meaning that particles interact at large, non-infinitesimal length scales. Moreover, the coefficients are singular and degenerate for large velocities. Many important questions, such as whether or not solutions become unbounded after a finite time, are still unanswered due to their mathematical complexity.
In this talk we concentrate on the mathematical results of the homogeneous Landau equation. We will first review existing results and open problems and in the second part of the talk we will focus on recent developments of well-posedness and regularity theory. This is a joint work with Nestor Guillen.

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Contact

Ian Tobasco

Date posted

Apr 21, 2021

Date updated

Apr 21, 2021

Speakers

Maria Pia Gualdani | (UT Austin)