L2-CONCENTRATION PHENOMENON FOR ZAKHAROV SYSTEM BELOW ENERGY NORM

DOI10.1142/S0219199709003272zbMath1209.35125arXivmath/0702181OpenAlexW2023667843MaRDI QIDQ3622802

Sijia Zhong, Daoyuan Fang

Publication date: 28 April 2009

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702181

zbMATH Keywords

global existenceblow up\(L^2\)-concentrationZakharov system in space dimension two

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44)

Related Items (1)

Low regularity global well-posedness for the two-dimensional Zakharov system

Cites Work

• L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
• The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
• Equations of Langmuir turbulence and nonlinear Schrödinger equation: Smoothness and approximation
• ``Mass concentration phenomenon for the nonlinear Schrödinger equation with the critical power nonlinearity. II
• Existence of solitary waves in higher dimensions
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I
• Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II
• On the Cauchy problem for the Zakharov system
• Cauchy problem for the \(L^2\)-critical nonlinear Schrödinger equation below \(H^1\)
• Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
• Multilinear estimates for periodic KdV equations, and applications
• Ground state mass concentration in the \(L^2\)-critical nonlinear Schrödinger equation below \(H^1\)
• Some remarks on Strichartz estimates for the homogeneous wave equation
• Rate of L2 concentration of blow-up solutions for the nonlinear schrödinger equation with critical power
• FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION
• On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations
• The nonlinear Schrödinger limit and the initial layer of the Zakharov equations

This page was built for publication: L²-CONCENTRATION PHENOMENON FOR ZAKHAROV SYSTEM BELOW ENERGY NORM