Wednesday, January 19, 2022 - 16:15 in ZOOM - Video Conference
Invariant Gibbs measures for a three-dimensional wave equation with a Hartree nonlinearity
A talk in the Oberseminar Analysis series by
Bjoern Bringmann
| Abstract: |
In this talk, we discuss the construction and invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree-nonlinearity.
In the first half of the talk, we construct the Gibbs measure and examine its properties. We discuss the mutual singularity of the Gibbs measure and the so-called Gaussian free field. In contrast, the Gibbs measure for one or two-dimensional wave equations is absolutely continuous with respect to the Gaussian free field. In the second half of the talk, we discuss the probabilistic well-posedness of the corresponding nonlinear wave equation, which is needed in the proof of invariance. This was the first theorem proving the invariance of a singular Gibbs measure for any dispersive equation.
If time permits, I will conclude the talk with an outlook on geometric wave equations.
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 |
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