Well-posedness results for the generalized Benjamin–Ono equation with small initial data

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Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations (2010, unknown): “Using the version of the Christ and Kiselev’s lemma in Molinet and Ribaud [34], Lemma 3, we obtain, ‖Tkh‖L2α x L∞T ≤ C2 +‖∂xh‖L1xL2T .”
Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations (2007, methodology): “[25] L. Molinet, F. Ribaud, Well posedness results for the generalized Benjamin–Ono equation with small initial data, J. Math.”
On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations (2003, methodology): “The version of this lemma that we use is the one presented and proved in [ MR ], [SmSo].”
On the Cauchy problem for higher-order nonlinear dispersive equations (2007, methodology): “Following the ideas in [14], we will derive linear estimates for the phase localized free and nonhomogeneous evolutions.”
Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data (2009, methodology): “Our idea follows Molinet and Ribaud [21], and Smith and Sogge [25].”
On the Cauchy Problem for the Generalized Korteweg-de Vries Equation (2003, background): “The proof of Lemma 2 can be found in Molinet and Ribaud (2003) inspired by Planchon (Private communication).”