On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations

By Carlos E. Kenig, Kenneth D. Koenig. 2003

150 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/21ffda03c8629d5aeaaa8ddb424b5b86368caf00

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Citations in the corpus

On well-posedness for the Benjamin–Ono equation (2005, methodology): “On the other hand, (1.1) has global weak L2 and H 1 2 solutions (Ginibre- Velo[6℄) and this result relies heavily on dispersive estimates for the nonlinear equation as well as ∗ Département de mathématiques, UMR 8628 du CNRS, Bât 425 Université Paris-Sud, F-91405 Orsay et Institut universitaire de F”
The Cauchy problem for the 3D Zakharov-Kuznetsov equation (2009, methodology): “Using maximal function estimates like in [13] for the Benjamin-Ono equation might improve our result but it is not obvious this will suffice to get an H(1) theory.”
Global well-posedness in L2 for the periodic Benjamin-Ono equation (2006, background): “The Cauchy problem on the real line has been extensively studied these last years (cf. [22], [1], [13], [21], [20], [16], [ 14 ]).”
On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map (2007, methodology): “The following proposition is a refined version of the Strichartz estimate, introduced by Koch and Tzvetkov [12] and improved by Kenig and Koenig [7] in the context of the Benjamin-Ono equation.”
Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation (2014, result): “We also refer to [1, 3, 7, 9, 13, 14, 15, 17, 18] for previous results on the topic, as well as to [4] where the Cauchy problem has been studied in functional spaces larger than L2.”
Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory (2004, methodology): “This has been improved by Kenig and Koenig [31] to s > 9/8 and more recently by Tao [45] to H 1(R).”
Global well-posedness of the Benjamin–Ono equation in low-regularity spaces (2005, background): “…initial-value problem has weak solutions in H 0 r ( R ), H 1 / 2 r ( R ), and H 1 r ( R ) (see [5], [25], and [18]) and is globally well-posed in H σr ( R ), σ ≥ 1 (see [22], as well as [7], [17], [12], and [8] for earlier local and global well-posedness results in higher regularity spaces).”
The IVP for the Benjamin-Ono equation in weighted Sobolev spaces (2010, methodology): “So we recall the result in [20] which affirms that for s > 9/8 ∂xu, ∂xv ∈ L1 ([0, T ] : L∞x (R)), (3.”
Nonlinear wave interactions for the Benjamin-Ono equation. (2004, background): “We first state a basic existence result for the Benjamin-Ono equation (see [1, 11, 17, 13, 15, 16]).”