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) |
|---|---|
| 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 1 2007 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering
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Global conservative solutions of the Camassa-Holm equation. / Bressan, Alberto; Constantin, Adrian.
In: Archive for Rational Mechanics and Analysis, Vol. 183, No. 2, 01.02.2007, p. 215-239.Research output: Contribution to journal › Review article
TY - JOUR
T1 - Global conservative solutions of the Camassa-Holm equation
AU - Bressan, Alberto
AU - Constantin, Adrian
PY - 2007/2/1
Y1 - 2007/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33846878957&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846878957&partnerID=8YFLogxK
U2 - 10.1007/s00205-006-0010-z
DO - 10.1007/s00205-006-0010-z
M3 - Review article
VL - 183
SP - 215
EP - 239
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -