On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
By Adrian Constantin, Joachim Escher. 2000
366 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/71e24f2138624cac59a315f6adff412538758e30
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In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “The blow up phenomena of the periodic Camassa–Holm equation were investigated in a number of papers (see [9,13,15,16] and references therein).”
- On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, background): “The main results in this section are in analogy with results established for the CH equation in [7, 12].”
- Geodesic flow on the diffeomorphism group of the circle (2003, background): “Some solutions of the Camassa–Holm equation exist globally in time [5], whereas others develop singularities in finite time [6].”
- Classical solutions of the periodic Camassa—Holm equation (2002, result): “In the next section we begin with a review of local well-posedness results in the framework of Sobolev spaces and give a new persistence of solutions result stronger than those of [ ConE2 ] but similar to that obtained independently in [D].”
- Global existence and blow-up phenomena for the weakly dissipative Novikov equation (2012, methodology): “It iswell-known that the Camassa–Holm equation ut − utxx + 3uux − 2uxuxx − uuxxx = 0, t > 0, x ∈ R, possesses global existence, the precise blow-up scenario, blow-up set and blow-up rate for the strong solutions [10–13].”
- Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, background): “Well-posedness and wave breaking of the CH equation were studied extensively, and many interesting results have been obtained, see [7–11,33] for example.”
- Ill-posedness of the Camassa–Holm and related equations in the critical space (2018, background): “kov equation we have the similar blow-up results. The blow-up of smooth solutions for CH can only occur in the form of wave breaking: the solution remains bounded but its slope becomes unbounded (see [7, 10, 11]). Lemma2.2([8]).Assume u 0(x) ∈ H3(K) is a real-valued odd function and u′ 0(0) < 0. ”
- Initial Boundary Value Problems of the Camassa–Holm Equation (2008, neutral): “For the periodic Camassa–Holm equation (Constantin and Escher, 2000), blow up of the solution ũ = ũ · ũ0 to Eq.”
- 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].”