Wave-breaking criterion for the Rotation-Camassa-Holm equation
A wave-breaking criterion for the Rotation-Camassa-Holm(R-CH)equation is studied in Sobolev space Hs(R).Firstly,we derive a Riccati-type inequality by the Lagrange flow,Young's inequality,Sobolev inequality and conserved quantity.Then,by using the relevant results of the analysis of Riccati type inequality,a wave breaking criterion for the R-CH equation is obtained,i.e.,an initial condition that causes the solution of the equation to lead to wave breaking within a finite time.
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