Scattering for the Zakharov-Kuznetsov equation
A talk in the Oberseminar Analysis series by
Philippe Anjolras
| Abstract: | The Zakharov-Kuznetsov equation is a model of propagation of acoustic waves in a plasma. Mathematically, it corresponds to a multi-dimensional generalisation of the Korteweg-de-Vries equation, but it is anisotropic. In particular, its linear part enjoys dispersive properties and one expects that it satisfies a property of scattering: if the initial data is small enough, the solution should behave asymptotically as a linear solution.
In this talk, I will introduce this equation and two results of scattering, in 2D and 3D, and will explain how to adapt the method of space-time resonances introduced by Germain-Masmoudi-Shatah to overcome the difficulties caused by anisotropy. Zoom: https://uni-bielefeld.zoom-x.de/j/64951709096?pwd=EfJynCkou8bBw77CsNYMuh88IrKazJ.1 Within the CRC this talk is associated to the project(s): A1 |