Global existence and asymptotic behaviour in time of small solutions to the elliptic - hyperbolic Davey - Stewartson system

DOI10.1088/0951-7715/9/6/001zbMath0906.35096OpenAlexW1987918108MaRDI QIDQ3841245

Nakao Hayashi, Hitoshi Hirata

Publication date: 16 February 1999

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/9/6/001

zbMATH Keywords

weighted Sobolev spacedecay estimateselliptic-hyperbolic Davey-Stewartson systemglobal existence of small solutions

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items (14)

Low-regularity integrator for the Davey-Stewartson system: elliptic-elliptic case ⋮ Numerical study of the Davey-Stewartson system ⋮ Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data ⋮ Numerical study of Davey–Stewartson I systems ⋮ On the integrability of a generalized Davey-Stewartson system ⋮ Existence and blow-up of solutions to degenerate Davey–Stewartson equations ⋮ Dromions of flexural-gravity waves ⋮ The Cauchy problem for the elliptic-hyperbolic Davey-Stewartson system in Sobolev space ⋮ IST Versus PDE: A Comparative Study ⋮ A global existence and blow-up threshold for Davey-Stewartson equations in \(\mathbb{R}^3\) ⋮ Local well-posedness for the Davey-Stewartson equation in a generalized Feichtinger algebra ⋮ On the two-power nonlinear Schrödinger equation with non-local terms in Sobolev-Lorentz spaces ⋮ A numerical approach to Blow-up issues for Davey-Stewartson II systems ⋮ Remarks on the full dispersion Davey-Stewartson systems

This page was built for publication: Global existence and asymptotic behaviour in time of small solutions to the elliptic - hyperbolic Davey - Stewartson system