Global Conservative Solutions of the Camassa–Holm Equation
Alberto Bressan and Adrian Constantin
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.
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- Alberto Bressan,
- Adrian Constantin,
- Publishing information:
- Submitted by:
April 14 2005.
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