Dispersive estimates for the Dirac-Coulomb equation
A talk in the Oberseminar Analysis series by
Federico Cacciafesta from Padua
| Abstract: | The Dirac-Coulomb equation represents a relevant model in relativistic quantum mechanics, as well as a challenging one from the point of view of dispersive PDEs: indeed, the Coulomb potential is critical with respect to the scaling of the (massless) Dirac operator, and therefore proving dispersive estimates is a complicated task. In this talk, after introducing the main features of the operator in the setting of dispersive PDEs, I will present some families of dispersive estimates (namely local smoothing and Strichartz estimates with loss of angular derivatives) that we recently obtained, trying to highlight the main differences and difficulties with respect to its non-relativistic counterpart, the Schroedinger equation.
The talk is based on works in collaboration with E. Séré (Paris CEREMADE) and J. Zhang (Beijing Institute of Technology). Zoom Meeting ID: 986 0677 6055 Passcode: 430747 $\href{https://uni-bielefeld.zoom.us/j/98606776055?pwd=azBFdUVaQnJMU01tWjZUVEdxN2x5Zz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A1 |