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Abstract In this study, we consider the Cauchy problem for the second-order Camassa–Holm equation with periodic initial data u 0 . Using the vanishing viscosity method, the local weak solution… Click to show full abstract
Abstract In this study, we consider the Cauchy problem for the second-order Camassa–Holm equation with periodic initial data u 0 . Using the vanishing viscosity method, the local weak solution of the equation is obtained in the finite energy space. A continuous semigroup of weak conservative solutions in Lagrangian coordinates is constructed. In particular, for any two solutions u ( t ) and v ( t ) of the equation, a Lipschitz metric d D is constructed with the property that d D ( u ( t ) , v ( t ) ) ≤ e C t d D ( u 0 , v 0 ) .
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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