Global Conservative Solutions of the Camassa–Holm Equation |
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Authors: | Alberto Bressan Adrian Constantin |
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Institution: | (1) Department of Mathematics, Pennsylvania State University, University Park, 16802, U.S.A.;(2) School of Mathematics, Trinity College Dublin, Dublin 2, Ireland;(3) Department of Mathematics, Lund University, 22100 Lund, Sweden |
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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. |
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Keywords: | |
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