ANALYSIS OF FLUIDS AND RELATED TOPICS: On a linear Landau equation with the specular reflection boundary condition and the Sp estimates, Timur Yastrzhembskiy, Brown University

Analysis of Fluids and Related Topics
  • Timur Yastrzhembskiy
  • Brown University
  • On a linear Landau equation with the specular reflection boundary condition and the Sp estimates
Oct 6, 2022
3 pm
Fine Hall 314

Title: On a linear Landau equation with the specular reflection boundary condition and the SpSp estimates

Abstract: Motivated by studies of the nonlinear kinetic Landau equation in a bounded domain, we investigate the linearized equation with the specular reflection boundary condition. To study the regularity of the solution near the boundary, one needs to develop the SpSp theory (Calderon-Zygmund theory) for the degenerate Kolmogorov-Fokker-Planck equation with `irregular' coefficients in the whole space. This is joint work with Hongjie Dong and Yan Guo. In the second part of the talk, I explain how to derive such SpSp estimates using a `kernel-free' approach. This is joint work with Hongjie Dong.Motivated by studies of the nonlinear kinetic Landau equation in a bounded domain, we investigate the linearized equation with the specular reflection boundary condition. To study the regularity of the solution near the boundary, one needs to develop the SpSp theory (Calderon-Zygmund theory) for the degenerate Kolmogorov-Fokker-Planck equation with `irregular' coefficients in the whole space. This is joint work with Hongjie Dong and Yan Guo. In the second part of the talk, I explain how to derive such SpSp estimates using a `kernel-free' approach.

This is joint work with Hongjie Dong.