Wednesday, December 11, 2024 - 16:15 in V4-116 and Zoom
Endpoint Strichartz estimates and small data scattering for the cubic Dirac equations on a curved background
A talk in the Oberseminar Analysis series by
Seokchang Hong from Uni Bielefeld
| Abstract: |
The initial value problems of nonlinear Dirac equations have been extensively studied. In this talk, we shall enlighten our understanding further into the Dirac equations on curved space-time. We first introduce the Dirac operator in terms of covariant derivatives. A typical approach of studying the Dirac equations is to exploit the projection operator defined by Fourier multipliers. Unfortunately, since the gamma matrices are no longer constant matrices on a curved space-time, we have to define the operators in terms of pseudo-differential calculus. Equipped with these operators, the Dirac equations can be reformulated into the half-Klein-Gordon equations with variable coefficients. We establish the endpoint Strichartz estimates for the half-Klein-Gordon equation with an assumption of small perturbation and then obtain the global well-posedness and scattering for the cubic Dirac equation on an asymptotically flat space-time.
This work is joint with Sebastian Herr.
$\href{https://uni-bielefeld.zoom-x.de/j/68601123008?pwd=3B0C4nRNJveeJ71WQ1caCai3MbXTwA.1}{\textbf{Join Zoom Meeting}}$
Meeting-ID: 686 0112 3008
Passwort: 867330
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