# American Institute of Mathematical Sciences

March  2018, 38(3): 1605-1613. doi: 10.3934/dcds.2018066

## Wave breaking of periodic solutions to the Fornberg-Whitham equation

 Fakultät für Mathematik, Universität Wien, Austria

Received  September 2017 Revised  October 2017 Published  December 2017

Based on recent well-posedness results in Sobolev (or Besov spaces) for periodic solutions to the Fornberg-Whitham equations we investigate here the questions of wave breaking and blow-up for these solutions. We show first that finite maximal life time of a solution necessarily leads to wave breaking. Second, we prove that for a certain class of initial wave profiles the corresponding solutions do indeed blow-up in finite time.

Citation: Günther Hörmann. Wave breaking of periodic solutions to the Fornberg-Whitham equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1605-1613. doi: 10.3934/dcds.2018066
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