|
|
| |
| On Local Singularities in Ideal Potential Flows with Free Surface |
| |
Citation： |
Jian-Guo LIU,Robert L. PEGO.On Local Singularities in Ideal Potential Flows with Free Surface[J].Chinese Annals of Mathematics B,2019,40(6):925~948 |
| Page view： 528
Net amount： 406 |
Authors： |
Jian-Guo LIU; Robert L. PEGO |
Foundation： |
This work was supported by the National Science
Foundation under NSF Research Network Grant RNMS11-07444 (KI-Net),
the NSF Grants DMS-1514826, DMS-1812573, DMS-1515400, DMS-1812609
and the Simons Foundation under Grant 395796. |
|
|
| Abstract： |
Despite important advances in the mathematical analysis of the Euler
equations for water waves, especially over the last two decades, it
is not yet known whether local singularities can develop from smooth
data in well-posed initial value problems. For ideal free-surface
flow with zero surface tension and gravity, the authors review
existing works that describe ``splash singularities'', singular
hyperbolic solutions related to jet formation and ``flip-through'',
and a recent construction of a singular free surface by Zubarev and
Karabut that however involves unbounded negative pressure. The
authors illustrate some of these phenomena with numerical
computations of 2D flow based upon a conformal mapping formulation.
Numerical tests with a different kind of initial data suggest the
possibility that corner singularities may form in an unstable way
from specially prepared initial data. |
Keywords： |
Incompressible flow, Water wave equations, Splash singularity,Flip-through, Dirichlet hyperbolas, Conformal mapping |
Classification： |
76B07, 76B10, 35L67, 30C30 |
|
|
Download PDF Full-Text
|
|
|
|
