论文标题
关于Zakharov-Kuznetsov方程解决方案解决方案的规律性传播
On the propagation of regularity for solutions of the Zakharov-Kuznetsov equation
论文作者
论文摘要
在这项工作中，我们研究了与zakharov-kuznetsov-（ZK）方程相关的初始价值问题，以$ n- $ dimensional设置，$ n \ geq 2。 众所周知，ZK方程的解决方案在$ 2D $中，$ 3D $ case验证了特殊的规律性属性。更确切地说，关于半个空间家族的初始数据的规律性以无限的速度传播。我们在这项工作中的目的是将此分析扩展到案例，即初始数据的规律性以分数尺度衡量。为了描述这种现象，我们提出了新的本地化公式，使我们能够在欧几里得空间的某些类别的子集上描绘解决方案的规律性。
In this work, we study some special properties of smoothness concerning to the initial value problem associated with the Zakharov-Kuznetsov-(ZK) equation in the $n-$ dimensional setting, $n\geq 2.$ It is known that the solutions of the ZK equation in the $2d$ and $3d$ cases verify special regularity properties. More precisely, the regularity of the initial data on a family of half-spaces propagates with infinite speed. Our objective in this work is to extend this analysis to the case in that the regularity of the initial data is measured on a fractional scale. To describe this phenomenon we present new localization formulas that allow us to portray the regularity of the solution on a certain class of subsets of the euclidean space.
