Strichartz estimates for a Maxwell equation
A talk in the Oberseminar Analysis series by
Roland Schnaubelt from KIT
| Abstract: | We establish global-in-time Strichartz estimates for the Maxwell system
on $R^3$ with scalar time-independent coefficients of class $C^2$. For
the coefficients we require decay conditions at infinity and a one-sided
bound on their radial derivative, ensuring non-trapping. There is no
global smallness assumption.
Using its divergence equations, the Maxwell system is rewritten as a
wave system with coefficients in front of the Laplacian and a coupling
in the first-order terms. Our approach relies on known local-in-time
Strichartz estimates for the wave equation due to Metcalfe-Tataru and
new global-in-time weighted energy estimates for our wave system. The
latter rely on a detailed analysis of the corresponding Helmholtz
problem. This is joint work with Piero D'Ancona (Rome). |