Abstract
The two-dimensional free boundary problem for incompressible irrota- tional water waves without surface tension is proved to have exactly eight nontrivial conservation laws. Included is a discussion of what constitutes a conservation law for a general free boundary problem, and a characterization of conservation laws for two-dimensional free boundary problems involving a harmonic potential proved using elementary methods from complex analysis.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 353-380 |
| Number of pages | 28 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 277 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1983 |
Keywords
- Completely integrable
- Conservation law
- Free boundary problem
- Harmonic function
- Water waves