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Blow-up for the b-family of equations

Published 15 Jul 2014 in math.AP | (1407.4084v3)

Abstract: In this paper we consider the $b$-family of equations on the torus $u_t- u_{txx}+ (b+1) u u_x=b u_x u_{xx} + u u_{xxx}$, which for appropriate values of $b$ reduces to well-known models, such as the Camassa-Holm equation or the Degasperis-Procesi equation. We establish a local-in-space blow-up criterion

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