Global dynamics below the ground state energy for the Zakharov system in the 3D radial case

DOI10.1016/J.AIM.2013.02.008zbMath1284.35369arXiv1206.2457OpenAlexW1992452333MaRDI QIDQ387896

Kenji Nakanishi, Zihua Guo, Shu-xia Wang

Publication date: 17 December 2013

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2457

zbMATH Keywords

scatteringsolitonsground stateblow upnonlinear wave equationsZakharov systemHamiltonian and variational structuresLangmuir turbulence in plasma

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Statistical mechanics of plasmas (82D10) Blow-up in context of PDEs (35B44)

Related Items (16)

Randomized final-state problem for the Zakharov system in dimension three ⋮ Scattering for the Zakharov system in 3 dimensions ⋮ Generalized Strichartz estimates and scattering for 3D Zakharov system ⋮ Scattering for the quadratic Klein-Gordon equations ⋮ Concentration compactness for the energy critical Zakharov system ⋮ The Zakharov system in dimension \(d \geq 4\) ⋮ Local well-posedness for the quantum Zakharov system in one spatial dimension ⋮ The fourth-order nonlinear Schrödinger limit for quantum Zakharov system ⋮ Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials ⋮ Scattering and blow-up for the focusing nonlinear Klein-Gordon equation with complex-valued data ⋮ Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect ⋮ Scattering for the quadratic beam equation with radial initial data ⋮ Semi-classical limit for the Quantum Zakharov system ⋮ Global well-posedness and scattering for the Zakharov system at the critical space in three spatial dimensions with small and radial initial data ⋮ The Zakharov system in 4D radial energy space below the ground state ⋮ Global Dynamics below the Ground State Energy for the Klein-Gordon-Zakharov System in the 3D Radial Case

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