Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity \(\overline{u}^2\)
From MaRDI portal
Publication:939221
DOI10.3934/cpaa.2008.7.1123zbMath1144.35047OpenAlexW2017154969MaRDI QIDQ939221
Publication date: 22 August 2008
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/cpaa.2008.7.1123
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for nonlinear higher-order PDEs (35G25)
Related Items (12)
An improved finite integration method for nonlocal nonlinear Schrödinger equations ⋮ Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions ⋮ Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation ⋮ On the Propagation of Regularity and Decay of Solutions to thek-Generalized Korteweg-de Vries Equation ⋮ Improved local well-posedness for the periodic ``good Boussinesq equation ⋮ The initial-boundary value problem for the Kawahara equation on the half-line ⋮ Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary ⋮ Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions ⋮ Invariance of the white noise for KdV ⋮ On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions ⋮ Local well-posedness for the quantum Zakharov system in three and higher dimensions ⋮ Ill-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity \(|u|^2\)
This page was built for publication: Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity \(\overline{u}^2\)
