Wednesday, April 22, 2026 - 16:15 in V4-116
Strichartz estimates and local well-posedness theory for the generalized Zakharov-Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$
A talk in the Oberseminar Analysis series by
Jakob Nowicki-Koth
| Abstract: |
The Zakharov-Kuznetsov equation (ZK) is a model for the
propagation of waves in plasma physics and can be viewed as a
two-dimensional analogue of the famous Korteweg-de Vries equation (KdV).
In this talk, we study the Cauchy problem associated with the
$k$-generalized Zakharov-Kuznetsov equation (gZK) posed on $\mathbb{R}
\times \mathbb{T}$, where $k \geq 2$ is an integer.
We establish several new Strichartz-type estimates in the framework of
Jean Bourgain's $X_{s,b}$ spaces, with the main contributions being an
almost optimal linear $L^4$-estimate and a family of bilinear
refinements of this bound.
As a direct application, we prove multilinear $X_{s,b}$-estimates that
lead to improved local well-posedness thresholds for gZK via a
fixed-point iteration.
Within the CRC this talk is associated to the project(s): A1 |
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