Low-regularity global solutions to nonlinear dispersive equations

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Blow-up of solutions to the DGH equation (2007, background): “Bourgain [3] proved that solutions to the KdV equation are global as long as the initial data is square integrable (see also [25,34] and references therein).”
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “It is shown that the KdV equation is globally well-posed for u0 ∈ L 2 (R) [ 43 ].”
The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations (2007, background): “[32]) so that the BBM family [5] does not model wave breaking [2, 30].”
Stability of peakons for the Degasperis‐Procesi equation (2007, unknown): “It is also noted that the KdV equation, unlike the CH equation or DP equation, does not have wave breaking phenomena [30].”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “[45].”
Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “It is known that the KdV equation is globally well-posed for u0 ∈ L2(S), see [31, 41].”
Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “It is noted that the KdV equation does not have wave breaking phenomena [36,48].”