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We investigate wave breaking for the Dullin-Gottwald-Holm equation and thetwo-component Dullin-Gottwald-Holm system. We establish a new blow-up criterionfor the general case $\gamma+c_0\alpha^2 \geq 0$ involving local-in-spaceconditions on the initial data.

The local criteria for blowup of the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system