论文标题
关于2D重力波的波湍流理论，I：确定性能量估计值
On the wave turbulence theory of 2D gravity waves, I: deterministic energy estimates
论文作者
论文摘要
本文我们的目标是对水波模型的波动力学方程（WKE）的波湍流和推导进行严格研究。近年来，在半线性模型的背景下，该问题引起了人们的关注，例如半线性schrödinger方程或多维KDV型方程。但是，我们这里的情况有所不同，因为水波方程是准线性的，由于不可避免的衍生化损失，无法通过Duhamel公式的迭代来构建解决方案。这是我们在2D重力波的背景下设计一种解决此问题的新策略的两篇论文中的第一篇。
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as semilinear Schrödinger equations or multi-dimensional KdV-type equations. However, our situation here is different since the water waves equations are quasilinear and the solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue, in the context of 2D gravity waves.
