Asymptotics and blow-up for mass critical nonlinear dispersive equations
Frank Merle
Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (2) : 579 -590.
Asymptotics and blow-up for mass critical nonlinear dispersive equations
The author considers mass critical nonlinear Schrödinger and Korteweg-de Vries equations. A review on results related to the blow-up of solution of these equations is given.
Dispersive nonlinear PDE / Criticality / Asymptotics / Blow-up / Global solution / Soliton
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| [5] |
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| [6] |
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| [7] |
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| [8] |
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| [9] |
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| [10] |
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| [11] |
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| [12] |
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| [13] |
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| [14] |
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| [15] |
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| [16] |
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| [17] |
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| [18] |
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| [19] |
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| [20] |
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| [21] |
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| [22] |
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| [23] |
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| [24] |
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| [25] |
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| [26] |
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| [27] |
Martel, Y., Merle, F. and Raphaël, P., Blow-up for critical gKdV equation I: Dynamics near the soliton, Acta Math., to appear. arXiv: 1204.4625 |
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Martel, Y., Merle, F. and Raphaël, P., Blow-up for critical gKdV equation II: Minimal mass solution, J.E.M.S., to appear. |
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Martel, Y., Merle, F. and Raphaël, P., Blow-up for critical gKdV equation III: Exotic regimes, Annali Scuola Norm. Sup. di Pisa, to appear. arXiv:1209.2510 |
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| [32] |
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| [33] |
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| [34] |
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| [35] |
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| [36] |
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| [37] |
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| [38] |
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| [39] |
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| [40] |
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| [41] |
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| [42] |
Merle, F., Raphaël, P. and Rodnianski, I., Type IIblow up for the energy supercritical NLS, preprint. |
| [43] |
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| [44] |
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| [45] |
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| [46] |
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| [47] |
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| [48] |
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| [49] |
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| [50] |
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| [51] |
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