A Simple Proof of Well-posedness for the Free-surface Incompressible Euler Equations
نویسندگان
چکیده
The purpose of this this paper is to present a new simple proof for the construction of unique solutions to the moving free-boundary incompressible 3-D Euler equations in vacuum. Our method relies on the Lagrangian representation of the fluid, and the anisotropic smoothing operation that we call horizontal convolution-by-layers. The method is general and can be applied to a number of other moving free-boundary problems.
منابع مشابه
Well-posedness of the Free-surface Incompressible Euler Equations with or without Surface Tension
We develop a new methodology for treating free boundary problems in mechanics, and use it to prove local-in-time well-posedness in Sobolev spaces for the freesurface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liqu...
متن کاملTransport and Instability for Incompressible and Inviscid Fluids
Incompressible perfect fluids are described by the Euler equations. We provide a new simple proof for well-posedness for velocities in C1;α and linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of C1;α is too fine for interesting questions about large time behavior.
متن کاملOn the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces
In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, a recovered proof of [7] for the incompressible Euler equation is given.
متن کاملA Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows
In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid MHD equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in [4], and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the out...
متن کاملWell-Posedness of the Free-Boundary Compressible 3-D Euler Equations with Surface Tension and the Zero Surface Tension Limit
We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and Friedrichs [8] as p(ρ) = αρ − β for consants γ > 1 and α, β > 0. The analysis is made difficult by two competing nonlinearities associated with the potential...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010