Local well-posedness and global analyticity for solutions of a generalized 0-equation

Abstract

In this work we study the Cauchy problem in Gevrey spaces for a generalized class of equations that contains the case $b=0$ of the $b$ -equation. For the generalized equation, we prove that it is locally well-posed for initial data in Gevrey spaces. Moreover, as we move to global well-posedness, we show that for a particular choice of the parameter in the equation the local solution is global analytic in both time and spatial variables.

Conserved quantities, continuation and compactly supported solutions of some shallow water models

“…The ideas of the present work have been recently employed in the study of unique continuation and compactly supported solutions of the BBM equation in [14] and a higher order generalisation of the 0−equation in [13,15]. While in [14,15] the results are concerned with Sobolev spaces, in [13] the problems are considered in Gevrey spaces. This latter work is the first one to use the ideas from the present work and those introduced in [30] to tackle problems in spaces other than Sobolev spaces.…”