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.
作者
邵鑫华
臧爱彬
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)
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).
