Partial regularity in time for the Landau equation with Coulomb interaction - Prof. Francois Golse (Ecole Polytechnique (Paris area, France))

作者:   来源:  时间:2021-05-20

Distinguished Lecture Series in Mathematics 系列数学前沿学术讲座

报告题目:Partial regularity in time for the Landau equation with Coulomb interaction

报告人:Prof. Francois Golse
             Ecole Polytechnique (Paris area, France)

报告时间 :2021年5月20日周四下午16:30-18:00

                 ZOOM URL:
                 Meeting ID: 974 1241 3730
                 Passcode: 321050

Francois Golse is currently Professor of Mathematics at Ecole Polytechnique (Paris area, France). His research interests are partial differential equations and mathematical physics, especially kinetic models and their connection with fluid dynamics, and, more recently, the quantum dynamics of large particle systems in the semiclassical and mean-field regimes. Together with Laure Saint-Raymond, he has been awarded the first PDE prize of the Society for Industrial and Applied Mathematics (SIAM) in 2006. He has given the 1993 Peccot Lectures at Collège de France (Paris), and the 2010 Harold Grad Lecture in the 27th International Symposium on Rarefied Gas Dynamics (Pacific Grove, USA). He has been a plenary speaker at the 2004 European Congress of Mathematics (Stockholm), and an invited speaker at the 2006 International Congress of Mathematicians (Madrid).

The Landau equation (1937) is the best known collisional kinetic model used in plasma physics. In 1998, Villani proved the global existence of a class of weak solutions of the Cauchy problem for the spatially homogeneous Landau equation with Coulomb interaction for all initial data of finite mass, energy and entropy. Such weak solutions are called “H solutions” since their definition involves the entropy production rate. To this date, it is unknown whether H solutions with smooth and rapidly decaying initial data remain smooth for all times or blow up in finite time. In this talk we prove that the set of times at which singularities may occur is “small”, specifically, of Hausdorff dimension at most 1/2 (result obtained in collaboration with M.P. Gualdani, C. Imbert and A. Vasseur). The talk will review some of the fundamental tools and techniques used to prove partial regularity, most notably the De Giorgi method (1957) which led to the solution of Hilbert’s 19th problem (on the analyticity of extremals in the calculus of variations).