Non-existence of global solutions for a quasilinear Benney system

DOI10.1007/S00021-009-0014-1zbMath1270.35358OpenAlexW2012670897MaRDI QIDQ361117

João-Paulo Dias, Filipe Oliveira, M. S. Figueira, Stanislav N. Antontsev

Publication date: 28 August 2013

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-009-0014-1

zbMATH Keywords

blow-upmixed problemcapillary/gravity waves

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (5)

The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system ⋮ On a quasilinear nonlocal Benney system ⋮ Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger-Korteweg-de Vries interactions on the half-line ⋮ A quasilinear system related with the asymptotic equation of the nematic liquid crystal's director field ⋮ The initial value problem for some hyperbolic-dispersive system

Cites Work

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• Existence of local strong solutions for a quasilinear Benney system
• Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
• The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Long-wave short-wave resonance for nonlinear geometric optics.
• Formation and Interaction of Sonic-Langmuir Solitons: Inverse Scattering Method
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• On two-dimensional packets of capillary-gravity waves
• A General Theory for Interactions Between Short and Long Waves
• The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• On a nonlinear Schrödinger equation arising in the theory of water waves

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