A sharp regularity result for the Euler equation with a free interface

[1]  I. Kukavica,et al.  On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition , 2016 .

[2]  M. Ifrim,et al.  Two dimensional water waves in holomorphic coordinates II: global solutions , 2014, 1404.7583.

[3]  Sijue Wu,et al.  Global wellposedness of the 3-D full water wave problem , 2011 .

[4]  Sijue Wu,et al.  Well-posedness in Sobolev spaces of the full water wave problem in 3-D , 1999 .

[5]  Sijue Wu,et al.  Well-posedness in Sobolev spaces of the full water wave problem in 2-D , 1997 .

[6]  I. Kukavica,et al.  ON THE 2D FREE BOUNDARY EULER EQUATION , 2012 .

[7]  F. Pusateri On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations , 2009, 0912.3296.

[8]  Hideaki Yosihara,et al.  Gravity Waves on the Free Surface of an Incompressible Perfect Fluid of Finite Depth , 1982 .

[9]  Nader Masmoudi,et al.  The zero surface tension limit of three-dimensional water waves , 2009 .

[10]  D. Ebin,et al.  On the Limit of Large Surface Tension for a Fluid Motion with Free Boundary , 2013, 1301.7507.

[11]  Well‐posedness for the linearized motion of an incompressible liquid with free surface boundary , 2001 .

[12]  Ben Schweizer,et al.  On the three-dimensional Euler equations with a free boundary subject to surface tension , 2005 .

[13]  Ping Zhang,et al.  On the free boundary problem of three‐dimensional incompressible Euler equations , 2008 .

[14]  S. Shkoller,et al.  A simple proof of well-posedness for the free-surfaceincompressible Euler equations , 2010 .

[15]  J. K. Hunter,et al.  Two Dimensional Water Waves in Holomorphic Coordinates , 2014, 1401.1252.

[16]  S. Čanić,et al.  Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy , 2015 .

[17]  C. Fefferman,et al.  Splash singularity for water waves , 2011, Proceedings of the National Academy of Sciences.

[18]  I. Kukavica,et al.  On the Local Existence and Uniqueness for the 3D Euler Equation with a Free Interface , 2017 .

[19]  F. Rousset,et al.  Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations , 2012, 1202.0657.

[20]  D. Christodoulou,et al.  S E M I N A I R E E quations aux , 2008 .

[21]  Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity , 2014, 1402.0464.

[22]  Thomas Alazard,et al.  On the water-wave equations with surface tension , 2009, 0906.4406.

[23]  Hideaki Yosihara Capillary-gravity waves for an incompressible ideal fluid , 1983 .

[24]  Boris Muha,et al.  Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls , 2012, Archive for Rational Mechanics and Analysis.

[25]  P. Germain,et al.  Global solutions for the gravity water waves equation in dimension 3 , 2009, 0906.5343.

[26]  Thomas Y. Hou,et al.  Growth rates for the linearized motion of fluid interfaces away from equilibrium , 1993 .

[27]  Thomas Alazard,et al.  Global solutions and asymptotic behavior for two dimensional gravity water waves , 2013, 1305.4090.

[28]  Fabio Pusateri,et al.  Global solutions for the gravity water waves system in 2d , 2013, Inventiones mathematicae.

[29]  J. T. Beale,et al.  The initial value problem for the navier-stokes equations with a free surface , 1981 .

[30]  Igor Kukavica,et al.  Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface , 2012 .

[31]  Igor Kukavica,et al.  On the local existence of the free-surface Euler equation with surface tension , 2016, Asymptot. Anal..

[32]  Zhifei Zhang,et al.  On the free boundary problem to the two viscous immiscible fluids , 2010 .

[33]  Masao Ogawa,et al.  FREE BOUNDARY PROBLEM FOR AN INCOMPRESSIBLE IDEAL FLUID WITH SURFACE TENSION , 2002 .

[34]  A. Tani Small-time existence for the three-dimensional navier-stokes equations for an incompressible fluid with a free surface , 1996 .

[35]  David Lannes,et al.  Well-posedness of the water-waves equations , 2005 .

[36]  Annalisa Quaini,et al.  A modular, operator‐splitting scheme for fluid–structure interaction problems with thick structures , 2013, 1311.3324.

[37]  Hans Lindblad Well-posedness for the motion of an incompressible liquid with free surface boundary , 2005 .

[38]  J. Shatah,et al.  Local Well-Posedness for Fluid Interface Problems , 2011 .

[39]  D. Ebin The equations of motion of a perfect fluid with free boundary are not well posed. , 1987 .

[40]  Jalal Shatah,et al.  Geometry and a priori estimates for free boundary problems of the Euler's equation , 2006 .

[41]  Daniel Coutand,et al.  Well-posedness of the free-surface incompressible Euler equations with or without surface tension , 2005 .

[42]  S. Čanić,et al.  Existence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition , 2015, 1505.04462.

[43]  D. Ebin,et al.  The free boundary Euler equations with large surface tension , 2015, 1506.02094.

[44]  Tosio Kato,et al.  Commutator estimates and the euler and navier‐stokes equations , 1988 .

[45]  I. Kukavica,et al.  A Regularity Result for the Incompressible Euler Equation with a Free Interface , 2014 .

[46]  Nader Masmoudi,et al.  The zero surface tension limit two‐dimensional water waves , 2005 .