Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]

DOI10.1016/j.anihpc.2010.01.006zbMath1188.35162arXiv0708.2011OpenAlexW1984403692MaRDI QIDQ975301

Herbert Koch, Sebastian Herr, Martin Hadac

Publication date: 9 June 2010

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2011

zbMATH Keywords

scatteringwell-posednessbilinear estimatesbounded \(p\)-variationKadomtsev-Petviashvili-II equationscale invariant space

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (only showing first 100 items - show all)

Lump, lumpoff, rogue wave, breather wave and periodic lump solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics ⋮ Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality ⋮ Low Regularity Local Well-Posedness for the Zero Energy Novikov–Veselov Equation ⋮ Scattering for the cubic Schrödinger equation in 3D with randomized radial initial data ⋮ On the support of solutions to the fifth-order Kadomtsev–Petviashvili II equation in three-dimensional space ⋮ Low regularity well-posedness for generalized Benjamin–Ono equations on the circle ⋮ Small data global solutions for the Camassa–Choi equations ⋮ CONDITIONAL LARGE INITIAL DATA SCATTERING RESULTS FOR THE DIRAC–KLEIN–GORDON SYSTEM ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ The Cauchy problem for a two-dimensional generalized Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces ⋮ Large time behavior and optimal decay estimate for solutions to the generalized Kadomtsev-Petviashvili-Burgers equation in 2D ⋮ Almost sure global well-posedness for the fourth-order nonlinear Schrödinger equation with large initial data ⋮ Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev-Petviashvili equation in fluid mechanics ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ Scattering and Nonscattering of the Hartree-Type Nonlinear Dirac System at Critical Regularity ⋮ Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation ⋮ Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS ⋮ Klein-Gordon-Schrödinger system: Dinucleon field ⋮ On long time behavior of the focusing energy-critical NLS on \(\mathbb{R}^d\times\mathbb{T}\) via semivirial-vanishing geometry ⋮ Well-posedness of the Kadomtsev-Petviashvili-II in the negative Sobolev space with respect to y direction ⋮ Low regularity well-posedness of KP-I equations: the three-dimensional case ⋮ On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation ⋮ The Phase Shift of Line Solitons for the KP-II Equation ⋮ Global Well-Posedness and Scattering for Mass-Critical, Defocusing, Infinite Dimensional Vector-Valued Resonant Nonlinear Schrödinger System ⋮ On Scattering for the Defocusing Quintic Nonlinear Schrödinger Equation on the Two-Dimensional Cylinder ⋮ Internal Controllability of Nonlocalized Solution for the Kadomtsev--Petviashvili II Equation ⋮ The direct scattering problem for the perturbed Gr(1, 2) _⩾0 Kadomtsev–Petviash-vili II solitons ⋮ On the cubic NLS on 3D compact domains ⋮ Recent Progress on the Global Well-Posedness of the KPI Equation ⋮ Unnamed Item ⋮ Strichartz estimates for \(N\)-body Schrödinger operators with small potential interactions ⋮ Global well-posedness of partially periodic KP-I equation in the energy space and application ⋮ Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators ⋮ The cubic Dirac equation: small initial data in \({H^{\frac{1}{2}}(\mathbb R^2)}\) ⋮ Well-posedness for a quadratic derivative nonlinear Schrödinger system at the critical regularity ⋮ Small data scattering of semirelativistic Hartree equation ⋮ On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping ⋮ Global wellposedness in the energy space for the Maxwell-Schrödinger system ⋮ On small data scattering of Hartree equations with short-range interaction ⋮ Local well-posedness of critical nonlinear Schrödinger equation on Zoll manifolds of odd-growth ⋮ Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in four and more spatial dimensions ⋮ Bilinear auto-Bäcklund transformations and similarity reductions for a \((3+1)\)-dimensional generalized Yu-Toda-Sasa-Fukuyama system in fluid mechanics and lattice dynamics ⋮ Quantitative derivation and scattering of the 3D cubic NLS in the energy space ⋮ Remark on the semilinear ill-posedness for a periodic higher-order KP-I equation ⋮ Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows ⋮ Strichartz estimates for Schrödinger equations on irrational tori ⋮ Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\) ⋮ Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation ⋮ Random data theory for the cubic fourth-order nonlinear Schrödinger equation ⋮ Global well-posedness and scattering for the Dysthe equation in \(L^2(\mathbb{R}^2)\) ⋮ The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Well-posedness for the supercritical gKdV equation ⋮ Stability of line solitons for the KP-II equation in ℝ² ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ The Cauchy problem for the rotation-modified Kadomtsev-Petviashvili type equation ⋮ Scattering results for Dirac Hartree-type equations with small initial data ⋮ Retracted: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities ⋮ Adapted Function Spaces for Dispersive Equations ⋮ Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system ⋮ On short-time bilinear Strichartz estimates and applications to the Shrira equation ⋮ A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton ⋮ On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations ⋮ Existence of the periodic peaked solitary-wave solutions to the Camassa-Holm-Kadomtsev-Petviashvili equation ⋮ On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities ⋮ Global well-posedness for the fifth order Kadomtsev-Petviashvili II equation in three dimensional space ⋮ Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case ⋮ A local well-posed result for the fifth order KP-II initial value problem ⋮ Energy and local energy bounds for the 1-d cubic NLS equation in \(H^{-\frac{1}{4}}\) ⋮ MATRIX-MFO tandem workshop/small collaboration: Rough wave equations. Abstracts from the MATRIX-MFO tandem workshop/small collaboration held September 12--18, 2021 (hybrid meeting) ⋮ Asymptotic stability of small ground states for NLS under random perturbations ⋮ Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\) ⋮ Almost sure well-posedness and scattering of the 3D cubic nonlinear Schrödinger equation ⋮ Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces ⋮ Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data ⋮ Global well-posedness for the KP-II equation on the background of a non-localized solution ⋮ On the stochastic nonlinear Schrödinger equations with nonsmooth additive noise ⋮ Conserved energies for the one dimensional Gross-Pitaevskii equation ⋮ Almost sure local well-posedness for the supercritical quintic NLS ⋮ Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold ⋮ Small Data Scattering for Cubic Dirac Equation with Hartree Type Nonlinearity in $\mathbb{R}^{1+3}$ ⋮ Stability of the line soliton of the KP-II equation under periodic transverse perturbations ⋮ Local wellposedness for the critical nonlinear Schrödinger equation on \( \mathbb{T}^3 \) ⋮ On the division problem for the wave maps equation ⋮ Small data scattering for semi-relativistic equations with Hartree type nonlinearity ⋮ Small data scattering of 2d Hartree type Dirac equations ⋮ On global-in-time Strichartz estimates for the semiperiodic Schrödinger equation ⋮ Global wellposedness for the energy-critical Zakharov system below the ground state ⋮ On a two dimensional nonlocal shallow-water model ⋮ Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases ⋮ Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on \(\mathbb{T}^3\) ⋮ Well-posedness of the fifth order Kadomtsev-Petviashvili I equation in anisotropic Sobolev spaces with nonnegative indices ⋮ Transference of bilinear restriction estimates to quadratic variation norms and the Dirac-Klein-Gordon system ⋮ On the 1D cubic nonlinear Schrödinger equation in an almost critical space ⋮ Conserved energies for the cubic nonlinear Schrödinger equation in one dimension ⋮ On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy ⋮ On global well-posedness and scattering for the massive Dirac-Klein-Gordon system ⋮ On the local regularity of the KP-I equation in anisotropic Sobolev space ⋮ Energy dispersed large data wave maps in \(2+1\) dimensions ⋮ IST Versus PDE: A Comparative Study ⋮ Global well-posedness and global attractor for two-dimensional Zakharov-Kuznetsov equation

Cites Work

• Scattering for the quartic generalised Korteweg-de Vries equation
• Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation
• Local well posedness for modified Kadomstev-Petviashvili equations.
• Degenerative dispersion laws, motion invariants and kinetic equations
• Transverse nonlinear instability for two-dimensional dispersive models
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• On the Cauchy problem for the Zakharov system
• Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
• On the cauchy problem for kadomtsev-petviashvili equation
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Dispersive estimates for principally normal pseudodifferential operators
• Asymptotic stability of solitons of the subcritical gKdV equations revisited
• Finite-dimensional perturbations of Volterra operators
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
• Well-posedness for the Kadomtsev-Petviashvili II equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]