On the well-posedness of the generalized Korteweg-de Vries equation in scale-critical lr-space

DOI10.2140/apde.2016.9.699zbMath1342.35309arXiv1507.01323OpenAlexW3099237610MaRDI QIDQ301923

Jun-Ichi Segata, Satoshi Masaki

Publication date: 4 July 2016

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01323

zbMATH Keywords

generalized Korteweg-de Vries equationscattering problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity ⋮ On Gagliardo-Nirenberg type inequalities in Fourier-Herz spaces ⋮ Refinement of Strichartz Estimates for Airy Equation in Nondiagonal Case and its Application ⋮ Large data mass-subcritical NLS: critical weighted bounds imply scattering ⋮ On the scattering of subcritical defocusing generalized Korteweg-de Vries equation ⋮ A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces ⋮ Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation ⋮ Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions ⋮ Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in \(\widehat{L^p}\)-spaces ⋮ The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space ⋮ Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation