Wave breaking for a periodic shallow water equation

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Blow-up of solutions to the DGH equation (2007, methodology): “In [38], the author found the best constant for the Sobolev embedding ‖f ‖L∞ C‖f ‖H 1 .”
On Solutions to a Two‐Component Generalized Camassa‐Holm Equation (2010, unknown): “Furthermore, in [15], Zhou has proved ‖u‖(2)L∞(S) ≤ c1‖u‖(2)H 1(S), On the other hand, by the explicit representation of G(x), assume that x ≤ 1, we have (G ∗ ρ(2))(x, t) = 1 2 sin h(1/2) ∫ x”
Local well‐posedness and blow‐up criteria of solutions for a rod equation (2005, background): “Moreover, wave breaking for a large class of initial data has been established in [3, 4, 5, 14, 15, 21, 22].”
Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “2 Secondly, let us recall the best constant for a Sobolev inequality proved in [20].”
A new asymptotic behavior of solutions to the Camassa-Holm equation (2012, background): “Moreover, conditions which guarantee their global existence and wave breaking for a large class of initial data has been established in [3, 7, 13, 14].”