Codimension one threshold manifold for the critical gKdV equation

DOI10.1007/s00220-015-2509-3zbMath1336.35315arXiv1502.04594OpenAlexW3102026460MaRDI QIDQ261639

Yvan Martel, Frank Merle, Kenji Nakanishi, Pierre Raphaël

Publication date: 24 March 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.04594

zbMATH Keywords

blowing upgKdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Blow-up in context of PDEs (35B44) Soliton solutions (35C08)

Related Items (21)

Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes ⋮ On asymptotic dynamics for \(L^2\) critical generalized KdV equations with a saturated perturbation ⋮ Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation ⋮ Construction of Multibubble Solutions for the Critical GKDV Equation ⋮ Blow-up solutions forL²supercritical gKdV equations with exactlykblow-up points ⋮ Full family of flattening solitary waves for the critical generalized KdV equation ⋮ On asymptotic stability of the sine-Gordon kink in the energy space ⋮ Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation ⋮ Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schrödinger equation ⋮ Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ On blow-up and dynamics near ground states for some semilinear equations ⋮ Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation ⋮ Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions ⋮ On continuation properties after blow-up time for \(L^2\)-critical gKdV equations ⋮ On melting and freezing for the 2D radial Stefan problem ⋮ Dynamics near the solitary waves of the supercritical gKDV equations ⋮ Center stable manifolds around line solitary waves of the Zakharov-Kuznetsov equation with critical speed ⋮ Description and classification of \(2\)-solitary waves for nonlinear damped Klein-Gordon equations ⋮ Strongly anisotropic type II blow up at an isolated point ⋮ On the Stability of Type I Blow Up For the Energy Super Critical Heat Equation

Cites Work

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• Blow up for the critical gKdV equation. II: Minimal mass dynamics
• Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation
• Invariant manifolds and dispersive Hamiltonian evolution equations
• New estimates for a time-dependent Schrödinger equation
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Scattering for the quartic generalised Korteweg-de Vries equation
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Threshold solutions for the focusing 3D cubic Schrödinger equation
• Non-generic blow-up solutions for the critical focusing NLS in 1-D
• Saddle points and instability of nonlinear hyperbolic equations
• A Liouville theorem for the critical generalized Korteweg-de Vries equation
• Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
• Small data scattering and soliton stability in \(\dot{H}^{-1/6}\) for the quartic KdV equation
• Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton
• Center-stable manifold of the ground state in the energy space for the critical wave equation
• Stable manifolds for an orbitally unstable nonlinear Schrödinger equation
• Global dynamics above the ground state energy for the cubic NLS equation in 3D
• Threshold phenomenon for the quintic wave equation in three dimensions
• Existence of blow-up solutions in the energy space for the critical generalized KdV equation
• The instability of Bourgain-Wang solutions for the <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> critical NLS
• Blow up for the critical gKdV equation III: exotic regimes
• A critical center-stable manifold for Schrödinger's equation in three dimensions
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation
• Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
• Instability of solitons for the critical generalized Korteweg-de Vries equation

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