Critical nonlinear Schrödinger equations with data in homogeneous weighted \(\mathbf L^2\) spaces

DOI10.1016/J.JMAA.2014.05.053zbMath1296.35171OpenAlexW2009445538MaRDI QIDQ2252328

Nakao Hayashi, Chun-Hua Li

Publication date: 17 July 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.05.053

zbMATH Keywords

nonlinear Schrödinger equationscritical nonlinearities\(\mathbf L^\infty\)-time decayhomogeneous weighted \(\mathbf L^2\) spaces

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (9)

The initial value problem for nonlinear Schrödinger equations with a dissipative nonlinearity in one space dimension ⋮ Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations ⋮ Nonlinear Schrödinger systems in 2d with nondecaying final data ⋮ Asymptotic behavior for solutions to the vector nonlinear Schrödinger equations ⋮ Critical nonlinear Schrödinger equations in higher space dimensions ⋮ Scattering for solutions of a dissipative nonlinear Schrödinger equation ⋮ Higher-order nonlinear Schrödinger equations with singular data ⋮ Dissipative nonlinear Schrödinger equations for large data in one space dimension ⋮ The obstacle problem for nonlinear noncoercive elliptic equations with \(L^1\)-data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation
• Existence of solutions for Schrödinger evolution equations
• On the asymptotic behavior of solutions of semi-linear wave equations
• Time dependent nonlinear Schrödinger equations
• A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equation in 2D.
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• Low regularity solutions for a 2D quadratic nonlinear Schrödinger equation
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space 𝑊^{𝑠,𝑝} for 𝑝<2
• Asymptotic Behavior of Solutions for Schrödinger Equations with Dissipative Nonlinearities
• On the Asymptotic Behavior of Nonlinear Wave Equations

This page was built for publication: Critical nonlinear Schrödinger equations with data in homogeneous weighted \(\mathbf L^2\) spaces