On the properties of weak solutions to elliptic equations with a drift term

• 主讲人：Tim Shilkin (St. Petersburg Branch of Steklov Mathematical Institute of RAS)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-05-25 21:00 - 2023-05-25 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/C0611FF18351179DC19875AD9B489896
Valid Until: 2027-06-30 23:59

 

Abstract: We investigate weak solutions to the Dirichlet problem for an elliptic equation with a drift term having a sign-defined divergence. Under minimal assumptions on the smoothness of the drift, we present results on the existence, uniqueness and local properties of weak solutions, as well as the possible relation of these results with the Navier-Stokes theory. Based on a joint work with M. Chernobai.

 

Bio: Tim Shilkin is a senior researcher at V.A. Steklov Mathematical Institute of RAS, St.-Petersburg, and at present, he is a visiting researcher at Max Planck Institute for Mathematics in the Sciences, Leipzig. After defending his Ph.D. thesis at the Steklov Institute in St. Petersburg, he joined the research group of Prof. O.A. Ladyzhenskaya at the same institute. His research interests lie in the area of PDEs and mathematical hydrodynamics. He is a recognized expert on the Navier-Stokes theory.