On Local Singularities in Ideal Potential Flows with Free Surface

作     者：Jian-Guo LIU Robert L.PEGO 

作者机构：Department of Physics and Department of MathematicsDuke UniversityDurhamNC 27708USA Department of Mathematical Sciences and Center for Nonlinear AnalysisCarnegie Mellon UniversityPittsburghPennsylvaniaPA 12513USA 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2019年第40卷第6期

页      面：925-948页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Science Foundation under NSF Research Network Grant RNMS11-07444(KI-Net) the NSF Grants DMS-1514826,DMS-1812573,DMS-1515400,DMS-1812609 the Simons Foundation under Grant 395796 

主　　题：Incompressible flow Water wave equations Splash singularity Flipthrough Dirichlet hyperbolas Conformal mapping 

摘      要：Despite important advances in the mathematical analysis of the Euler equations for water waves,especially over the last two decades,it is not yet known whether local singularities can develop from smooth data in well-posed initial value *** ideal free-surface flow with zero surface tension and gravity,the authors review existing works that describesplash singularities,singular hyperbolic solutions related to jet formation andflip-through,and a recent construction of a singular free surface by Zubarev and Karabut that however involves unbounded negative *** authors illustrate some of these phenomena with numerical computations of 2D flow based upon a conformal mapping *** tests with a different kind of initial data suggest the possibility that corner singularities may form in an unstable way from specially prepared initial data.