On the existence and uniqueness of smooth solution for a generalized Zakharov equation

DOI10.1016/j.jmaa.2009.10.045zbMath1185.35275OpenAlexW2035396032MaRDI QIDQ847771

Jingjun Zhang, Xue-ke Pu, Bo-ling Guo

Publication date: 19 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.10.045

zbMATH Keywords

self-generated magnetic fieldgeneralized Zakharov equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (19)

Approximation to the global solution of generalized Zakharov equations in \(\mathbb{R}^2\) ⋮ Initial boundary value problem for generalized Zakharov equations with nonlinear function terms ⋮ Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation ⋮ Schrödinger-improved Boussinesq system in two space dimensions ⋮ Equations of Langmuir turbulence and Zakharov equations: smoothness and approximation ⋮ Initial Boundary Value Problem for a Generalized Zakharov Equations ⋮ The time-periodic solutions to the modified Zakharov equations with a quantum correction ⋮ Global well-posedness and the classical limit of the solution for the quantum Zakharov system ⋮ Initial boundary value problem for generalized Zakharov equations. ⋮ On the limit behavior of the magnetic Zakharov system ⋮ Blow-up and nonlinear instability for the magnetic Zakharov system ⋮ Well-posedness for a class of generalized Zakharov system ⋮ Zakharov system in two space dimensions ⋮ Cauchy problem of the generalized Zakharov type system in \(\mathbf{R}^{2}\) ⋮ Exact 1-soliton solution of the Zakharov equation in plasmas withpower law nonlinearity ⋮ On global smooth solution for generalized Zakharov equations ⋮ Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect ⋮ Global existence for stochastic strongly dissipative Zakharov equations ⋮ On the convergence of the solution for a generalized Zakharov system

Cites Work

• Nonlinear Schrödinger equations and sharp interpolation estimates
• Energy convergence for singular limits of Zakharov type systems
• Semigroups of linear operators and applications to partial differential equations
• Compact sets in the space \(L^ p(0,T;B)\)
• The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
• Equations of Langmuir turbulence and nonlinear Schrödinger equation: Smoothness and approximation
• The Cauchy problem for a generalized Zakharov system
• On the Cauchy problem for the Zakharov system
• On global solution for a class of systems of multidimensional generalized Zakharov type equation
• An improved local well-posedness result for the one-dimensional Zakharov system
• Vorticity and Incompressible Flow
• FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION
• Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Nonlinear Schrödinger evolution equations
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• Global smooth solution for the Klein–Gordon–Zakharov equations
• The nonlinear Schrödinger limit and the initial layer of the Zakharov equations
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