On Local Singularities in Ideal Potential Flows with Free Surface


Journal Article

© 2019, The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg. 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.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Pego, RL

Published Date

  • November 1, 2019

Published In

Volume / Issue

  • 40 / 6

Start / End Page

  • 925 - 948

Electronic International Standard Serial Number (EISSN)

  • 1860-6261

International Standard Serial Number (ISSN)

  • 0252-9599

Digital Object Identifier (DOI)

  • 10.1007/s11401-019-0167-z

Citation Source

  • Scopus