Sharp ill-posedness result for the periodic Benjamin-Ono equation

DOI10.1016/j.jfa.2009.08.018zbMath1181.35246arXiv0811.0505OpenAlexW2028954785MaRDI QIDQ1039412

Luc Molinet

Publication date: 30 November 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.0505

zbMATH Keywords

Cauchy problemBenjamin-Ono equationcontinuity with respect to initial dataill-posedness result

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (9)

The Cauchy problem for the stochastic generalized Benjamin-Ono equation ⋮ Remarks on the Gibbs measures for nonlinear dispersive equations ⋮ Control and stabilization of the Benjamin-Ono equation in \(L^2(\mathbb T)\) ⋮ Weak continuity of the flow map for the Benjamin-Ono equation on the line ⋮ Well-posedness in energy space for the periodic modified Benjamin-Ono equation ⋮ Invariant measures and long time behaviour for the Benjamin-Ono equation. III ⋮ On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain ⋮ Local well-posedness for fourth order Benjamin-Ono type equations ⋮ Uniqueness properties of solutions to the Benjamin-Ono equation and related models

Cites Work

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• Internal waves of permanent form in fluids of great depth

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