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Zbl 1105.76013
Bressan, Alberto; Constantin, Adrian
Global conservative solutions of the Camassa-Holm equation. (English)
[J] Arch. Ration. Mech. Anal. 183, No. 2, 215-239 (2007). ISSN 0003-9527; ISSN 1432-0673/e

Summary: This paper develops a new approach to the analysis of 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 initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.

MSC 2000:: *76B15 Wave motions (fluid mechanics)
76B25 Solitary waves, etc. (inviscid fluids)
35Q35 Other equations arising in fluid mechanics
35Q51 Solitons

Keywords: fixed points; singularities; semigroup

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