A simple proof of well-posedness for the free-surface incompressible Euler equations. (English) Zbl 1210.35163
Summary: 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.
MSC:
35L65 | Hyperbolic conservation laws |
35L70 | Second-order nonlinear hyperbolic equations |
35L80 | Degenerate hyperbolic equations |
35Q35 | PDEs in connection with fluid mechanics |
35R35 | Free boundary problems for PDEs |
76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |