Friday, December 14, 2018 - 14:15 in D5-153
The Cauchy problem for the 2D Zakharov-Kuznetsov equation
A talk in the Oberseminar Analysis series by
Shinya Kinoshita
| Abstract: |
In this talk, we consider the Cauchy problem of the 2D Zakharov-Kuznetsov equation. Our aim is to show the well-posedness in a low regularity Sobolev space. In the proof of the crucial nonlinear estimate resonant interactions appear. Since their shape is very complicated (due to the linear part of Zakharov-Kuznetsov equation), it is challenging to treat all of them. To overcome this, we employ a nonlinear version of the Loomis-Whitney inequality and a suitable Whitney decomposition.
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