Abstract
The classical deep-water wave problem is to find a periodic traveling wave with a free surface of infinite depth. The main result is the construction of a global connected set of rotational solutions for a general class of vorticities. Each nontrivial solution on the continuum has a wave profile symmetric around the crests and monotone between crest and trough. The problem is formulated as a nonlinear elliptic boundary value problem in an unbounded domain with a parameter. The analysis is based on generalized degree theory and the global theory of bifurcation. The unboundedness of the domain renders consideration of approximate problems with stronger compactness properties.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1482-1521 |
| Number of pages | 40 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 37 |
| Issue number | 5 |
| DOIs | |
| State | Published - Jan 2006 |
| Externally published | Yes |
Keywords
- Bifurcation
- Leray-Schauder degree
- Nonlinear elliptic
- Vorticity
- Water waves
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics