The zero surface tension limit two‐dimensional water waves

By D. Ambrose, Nader Masmoudi. 2005

220 citations recorded by the source corpus.

Subfields: Earth-Surface Processes, Numerical Analysis, Oceanography

View Paper: https://www.semanticscholar.org/paper/ee407ed2a0ffcc5a6d664494220ad0b36da4dcfb

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In Earth-Surface Processes

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Citations in the corpus

Large time existence for 3D water-waves and asymptotics (2007, background): “More recently Coutand and Shkoller [12] and Shatah and Zeng [45] managed to remove the irrotationality condition and/or took into account surface tension effects (see also [3] for 1DH water-waves with surface tension).”
Contour Dynamics of Incompressible 3-D Fluids in a Porous Medium with Different Densities (2007, background): “A study of the two-dimensional case can be found in [2] due to Ambrose and Masmoudi.”
Almost global wellposedness of the 2-D full water wave problem (2009, background): “There has been much work recently concerning water waves with additional effects such as a nonzero surface tension, a bottom, and a bounded nonzero vorticity in the fluid region [1, 6, 7, 14, 24, 26, 28, 31, 41].”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, background): “[4] D. M. Ambrose and N. Masmoudi.”
Geometry and a priori estimates for free boundary problems of the Euler's equation (2006, background): “Recently D. Ambrose and N. Masmoudi [ AM05a ] proved that as ǫ → 0 solutions of the 2 dimensional irrotational problem converges to solutions of the zero surface problem by writing the equation in terms of the arc length of the fluid boundary.”
On the Euler equations of incompressible fluids (2007, methodology): “The modern well-posedness theory for free surfaces uses harmonic analysis and geometric PDEs ([3], [4], [35], [63], [65], [66], [102], [126], [127]) and is a subject in full swing.”
Finite time singularities for the free boundary incompressible Euler equations (2011, background): “~ (;t) jz~ (;t)j2 d: This choice of ~cwill ensure that jz~(;t)jdepends only on t. We will also dene an auxiliary function ~’(;t) analogous to the one introduced in [7] (for the linear case) and [4] (nonlinear case) which helps us to bound several of the terms that appear: ’~(;t) = Q2(;t)~!(;t) 2jz~ ”
On the free boundary problem of three‐dimensional incompressible Euler equations (2008, background): “Bibliography [1] Ambrose, D. M.; Masmoudi, N.”
On the Cauchy problem for gravity water waves (2012, methodology): “In fact, the systematic use of the Lagrangian formulation in most previous works [8,47,48], and the intensive use of Riemannian geometry tools (parallel transport, vector fields,.”
Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, background): “For multi-dimensional flows, parallel to a lot of activity and important progress in free surface boundary problems, in particular regarding incompressible fluids [2, 3, 4, 11, 20, 35, 58, 61, 64], more recently, there are some works trying to prove the local well-posedness of physical vacuum in 3D.”
Global wellposedness of the 3-D full water wave problem (2011, background): “We mention the following recent work on local wellposedness [1, 5, 6, 15, 18, 19, 21, 24, 34].”
Well-posedness of the free-surface incompressible Euler equations with or without surface tension (2005, background): “Later Ambrose [2] and Ambrose and Masmoudi [3] proved local well-posedness of the 2D water-wave problem with surface tension on the boundary replacing the Taylor sign condition.”