论文标题
在某些规律性的特性上
On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov Equation
论文作者
论文摘要
这项工作旨在研究与分散性广义的本杰明·扎明 - 扎克哈罗夫 - 库兹尼托夫方程相关的初始价值问题的一些平滑度。更确切地说，我们证明该模型的解决方案满足所谓的规律性传播。粗略地说，该原则指出，如果初始数据在半个空间的家庭上享有一些额外的平滑度，那么规律性就会以无限的速度传播。从这个意义上讲，我们证明，无论衡量这种超平面收集中额外规律性的规模如何，所有这些规律性也会通过该模型的解决方案传播。我们的分析主要是基于在平面某些区域中的均匀和非均匀衍生物相关的传播公式的推论。
This work aims to study some smoothness properties concerning the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation. More precisely, we prove that the solutions to this model satisfy the so-called propagation of regularity. Roughly speaking, this principle states that if the initial data enjoys some extra smoothness prescribed on a family of half-spaces, then the regularity is propagated with infinite speed. In this sense, we prove that regardless of the scale measuring the extra regularity in such hyperplane collection, then all this regularity is also propagated by solutions of this model. Our analysis is mainly based on the deduction of propagation formulas relating homogeneous and non-homogeneous derivatives in certain regions of the plane.
