论文标题
Zakharov-Kuznetsov方程的本地适应性在有限函数的背景下
Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function
论文作者
论文摘要
我们证明了二维Zakharov-kuznetsov方程的本地良好性，在$ h^s（\ Mathbb {r}^2）$中，在$ l^\ infty的背景下为$ s \ in [1,2] $ in [1,2] $满足一些自然的额外条件。该结果不仅为我们提供了一个框架来求解周围的ZK方程，例如，也围绕周期性解决方案，即考虑定期解决方案的局部非周期性扰动。此外，我们在能量空间$ h^1（\ mathbb {r}^2）$中显示了全球范围的良好性。
We prove the local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in $H^s(\mathbb{R}^2)$, for $s\in [1,2]$, on the background of an $L^\infty(\mathbb{R}^3)$-function $Ψ(t,x,y)$, with $Ψ(t,x,y)$ satisfying some natural extra conditions. This result not only gives us a framework to solve the ZK equation around a Kink, for example, but also around a periodic solution, that is, to consider localized non-periodic perturbations of periodic solutions. Additionally, we show the global well-posedness in the energy space $H^1(\mathbb{R}^2)$.
