具有移动底边界的水波问题的仿线性化  

Paralinearization of water waves with a moving bottom

作　　者：邵鑫华 臧爱彬[2] SHAO Xinhua;ZANG Aibin(School of Mathematics,Northwest University,Xi′an 710127,China;School of Mathematics and Computer Science and Center of Applied Mathematics,Yichun University,Yichun 336000,China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]宜春学院数学与计算机科学学院和宜春学院应用数学研究中心,江西宜春336000

出　　处：《纯粹数学与应用数学》2023年第2期159-185,共27页Pure and Applied Mathematics

基　　金：国家自然科学基金(12126359,12261093);江西省自然科学基金(20224ACB201004).

摘　　要：主要研究了带表面张力的无旋不可压缩重力水波问题,该水波的流动区域除了有自由上边界外,还具有给定的移动底边界.主要目的是利用仿微分方法对非线性水波问题的Zakharov表示进行仿线性化,关键在于处理Dirichlet-Neumann算子.借助Possion核定义正则映射来拉平边界会使仿线性化过程更加精细.这一仿线性化结果使非线性的水波方程成为线性系统,为研究具有移动底边界的水波方程适定性奠定了基础.In this paper,we study irrotational incompressible water waves with gravitation and surface tension in a moving domain,where there is a given moving bottom besides a free upper boundary.The main goal of this paper,using paradifferential caculus,is to paralinearize Zakharov formulation in nonlinear water wave problems.Defining a regularized mapping via Possion kernel to flatten the boundary makes the process of paralinearization more delicate.The paralinearization result makes the nonlinear water wave equations a linear system,which lays a foundation for studying the well-posedness of the water waves with a moving bottom.

关 键 词：水波问题 ZAKHAROV系统 仿线性化 Dirichlet-Neumann算子 移动底边界条件 

分 类 号：O186.1[理学—数学]