On Local Singularities in Ideal Potential Flows with Free Surface
| Autor: | Jian-Guo Liu, Robert L. Pego |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Ideal (set theory)
Jet (mathematics) Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Conformal map 01 natural sciences Euler equations 010104 statistics & probability symbols.namesake Flow (mathematics) Free surface symbols Initial value problem Gravitational singularity 0101 mathematics Mathematics |
| Zdroj: | Chinese Annals of Mathematics, Series B. 40:925-948 |
| ISSN: | 1860-6261 0252-9599 |
| DOI: | 10.1007/s11401-019-0167-z |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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