On the blow-up of solutions for the Fornberg-Whitham equation

Wave breaking of the water wave is important and interesting to physicist and mathematician. The present article is devoted to studying wave breaking (bounded solutions with unbounded derivative) of the Fornberg-Whitham equation. By virtue of the conservation law of the L2 norm of solutions which is found in this paper, two very useful a priori estimates are derived (see Theorem 2.1). Based on the L2-conservation and L∞-estimate of solutions, several blow-up phenomena of the Fornberg-Whitham equation on line R and on circle T are established.