Abstract
This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.
Original language | English (US) |
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Pages (from-to) | 215-239 |
Number of pages | 25 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 183 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2007 |
All Science Journal Classification (ASJC) codes
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering