Geometry and a priori estimates for free boundary problems of the Euler's equation

Jalal Shatah, Chongchun Zeng

Type: Article

Publication Date: 2007-08-28

Citations: 281

DOI: https://doi.org/10.1002/cpa.20213

Abstract

Abstract In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh‐Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh‐Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension. © 2007 Wiley Periodicals, Inc.

Locations

Communications on Pure and Applied Mathematics - View
CiteSeer X (The Pennsylvania State University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Geometry and a priori estimates for free boundary problems of the Euler's equation	2006	Jalal Shatah Chongchun Zeng
+	The free boundary problem for Euler’s equations	2019	Daniel Ginsberg
+	A PRIORI ESTIMATES FOR THE EULER EQUATION WITH A FREE BOUNDARY	2005	Ben Schweizer
+	A priori estimates for the free boundary problem of rotating Euler–Boussinesq equations with surface tension	2025	Xiaoling Hu
+ PDF Chat	On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid	2020	Marcelo M. Disconzi Chenyun Luo
+ PDF Chat	A Priori Estimates for the Compressible Euler Equations for a Liquid with Free Surface Boundary and the Incompressible Limit	2017	Hans Lindblad Chenyun Luo
+	On the Bernoulli Free Boundary Problem with Surface Tension	2019	Alfred Wagner
+	On the free boundary problem of three‐dimensional incompressible Euler equations	2007	Ping Zhang Zhifei Zhang
+ PDF Chat	Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics*	2022	Xumin Gu Chenyun Luo Junyan Zhang
+	The free boundary Euler equations with large surface tension	2016	Marcelo M. Disconzi David G. Ebin
+ PDF Chat	On the Limit of Large Surface Tension for a Fluid Motion with Free Boundary	2013	Marcelo M. Disconzi David G. Ebin
+	On a free boundary problem in fluid mechanics	1991	Ruxandra Stavre
+ PDF Chat	Uniform regularity for free-boundary Navier–Stokes equations with surface tension	2018	Tarek M. Elgindi Donghyun Lee
+ PDF Chat	ON THE LIMIT AS THE SURFACE TENSION AND DENSITY RATIO TEND TO ZERO FOR THE TWO-PHASE EULER EQUATIONS	2011	Fabio Pusateri
+	A free-boundary problem for Euler flows with constant vorticity on the sphere	2018	Sun-Chul Kim
+	On the local existence of the free-surface Euler equation with surface tension	2016	Mihaela Ignatova Igor Kukavica
+	Uniform Regularity for free-boundary navier-stokes equations with surface tension	2014	Tarek M. Elgindi Donghyun Lee
+	Uniform Regularity for free-boundary navier-stokes equations with surface tension	2014	Tarek M. Elgindi Donghyun Lee
+	On the Free Boundary to the Incompressible Euler Equations	2005	Ye-min Chen
+	On the Free Boundary to the Incompressible Euler Equations	2005	Chen YeMin

Works That Cite This (265)

Action	Title	Year	Authors
+	A priori estimates for the free boundary problem of incompressible neo-Hookean elastodynamics	2016	Chengchun Hao Dehua Wang
+ PDF Chat	Global Well-Posedness of Free Interface Problems for the Incompressible Inviscid Resistive MHD	2021	Yanjin Wang Zhouping Xin
+	p-Euler equations and p-Navier–Stokes equations	2018	Lei Li Jian‐Guo Liu
+ PDF Chat	Angled Crested Like Water Waves with Surface Tension: Wellposedness of the Problem	2021	Siddhant Agrawal
+ PDF Chat	On vacuum free boundary problems in ideal compressible magnetohydrodynamics	2023	Paolo Secchi Yuri Trakhinin Tao Wang
+ PDF Chat	Partial Justification of the Peregrine Soliton from the 2D Full Water Waves	2020	Qingtang Su
+ PDF Chat	On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid	2020	Marcelo M. Disconzi Chenyun Luo
+ PDF Chat	Large time existence for 3D water-waves and asymptotics	2007	Borys Álvarez-Samaniego David Lannes
+ PDF Chat	On the Cauchy problem for gravity water waves	2014	Thomas Alazard Nicolas Burq Claude Zuily
+ PDF Chat	On the Free Surface Motion of Highly Subsonic Heat-Conducting Inviscid Flows	2021	Tao Luo Huihui Zeng

Works Cited by This (22)

Action	Title	Year	Authors
+	Well-posedness of the water-waves equations	2005	David Lannes
+ PDF Chat	Well-posedness in Sobolev spaces of the full water wave problem in 3-D	1999	Sijue Wu
+	Groups of Diffeomorphisms and the Motion of an Incompressible Fluid	1970	David G. Ebin Jerrold E. Marsden
+ PDF Chat	Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits	1966	Vladimir I. Arnold
+	Well-posedness of the free-surface incompressible Euler equations with or without surface tension	2007	Daniel Coutand Steve Shkoller
+ PDF Chat	The Rigorous Approximation of Long-Wavelength Capillary-Gravity Waves	2002	Guido Schneider C. Eugene Wayne
+	Well-Posedness of Vortex Sheets with Surface Tension	2003	David M. Ambrose
+	FREE BOUNDARY PROBLEM FOR AN INCOMPRESSIBLE IDEAL FLUID WITH SURFACE TENSION	2002	Masao Ogawa Atusi Tani
+	An existence theory for water waves and the boussinesq and korteweg-devries scaling limits	1985	Walter Craig
+	On the three-dimensional Euler equations with a free boundary subject to surface tension	2005	Ben Schweizer