Existence of local strong solutions for a quasilinear Benney system

DOI10.1016/j.crma.2007.03.005zbMath1114.35002OpenAlexW2086143108MaRDI QIDQ883403

João-Paulo Dias, Filipe Oliveira, M. S. Figueira

Publication date: 4 June 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2007.03.005

zbMATH Keywords

Cauchy problem

Mathematics Subject Classification ID

Related Items (13)

Non-existence of global solutions for a quasilinear Benney system ⋮ Erratum to: ``Non-existence of global solutions for a quasilinear Benney system ⋮ On a coupled system of a Ginzburg–Landau equation with a quasilinear conservation law ⋮ The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system ⋮ On a quasilinear nonlocal Benney system ⋮ Decay of solutions for a class of nonlinear Schrödinger equations in $ \newcommand{\R}{\mathbb{R}} \R$ and the stability of shock profiles for a quasilinear Benney system ⋮ Global existence and blow-up for the classical solutions of the long-short wave equations with viscosity ⋮ Vanishing viscosity with short wave-long wave interactions for systems of conservation laws ⋮ Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system ⋮ A quasilinear system related with the asymptotic equation of the nematic liquid crystal's director field ⋮ On the Cauchy problem describing an electron-phonon interaction ⋮ A nonlinear model describing a short wave–long wave interaction in a viscoelastic medium ⋮ Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+

Cites Work

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• Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• Local existence of solution for the initial boundary value problem of fully nonlinear wave equation
• A General Theory for Interactions Between Short and Long Waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations

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