On ill-posedness for the generalized BBM equation

DOI10.3934/dcds.2014.34.4565zbMath1304.35603OpenAlexW2055893158MaRDI QIDQ476567

Xavier Carvajal, Mahendra Panthee

Publication date: 2 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.4565

zbMATH Keywords

well-posednessinitial value problemBBM equationill-posedness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (7)

Local well-posedness of generalized BBM equations with generalized damping on 1D torus ⋮ Sharp global well-posedness of the BBM equation in \(L^p\) type Sobolev spaces ⋮ Cauchy problem for the BBM equation in \(l^q L^2\) ⋮ Extended lifespan of the fractional BBM equation ⋮ Time-decay and Strichartz estimates for the BBM equation on modulation spaces: existence of local and global solutions ⋮ Long time behavior of a damped generalized BBM equation in low regularity spaces ⋮ Improved lower bounds of analytic radius for the Benjamin-Bona-Mahony equation

Cites Work

• On the ill-posedness result for the BBM equation
• Stability for the modified and fourth-order Benjamin-Bona-Mahony equations
• On the low regularity of the modified Korteweg-de Vries equation with a dissipative term
• Sharp well-posedness results for the BBM equation
• Well-posedness for regularized nonlinear dispersive wave equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Periodic Korteweg-de Vries equation with measures as initial data
• Comparisons between the BBM equation and a Boussinesq system
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space
• An evaluation of a model equation for water waves
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Remark on the local ill-posedness for KdV equation
• Model equations for long waves in nonlinear dispersive systems
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