On the existence of infinite energy solutions for nonlinear Schrödinger equations

DOI10.1090/S0002-9939-09-09773-1zbMath1166.35037arXiv0711.3441MaRDI QIDQ3629419

Pablo Braz e Silva, Lucas C. F. Ferreira, Elder Jesús Villamizar-Roa

Publication date: 27 May 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3441

zbMATH Keywords

existencenonlinear Schrödinger equationsinfinite energy solutions

Mathematics Subject Classification ID

Related Items (6)

Existence theory for the Boussinesq equation in modulation spaces ⋮ Self-similarity and asymptotic stability for coupled nonlinear Schrödinger equations in high dimensions ⋮ On the Davey-Stewartson system with singular initial data ⋮ On the two-power nonlinear Schrödinger equation with non-local terms in Sobolev-Lorentz spaces ⋮ Global existence for Schrödinger–Debye system for initial data with infinite 𝐿²-norm ⋮ Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces

Cites Work

• Self-similar solutions, uniqueness and long-time asymptotic behavior for semilinear heat equations.
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• On the global Cauchy problem for some nonlinear Schrödinger equations
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
• A NOTE ON THE NONLINEAR SCHRÖDINGER EQUATION IN WEAK L^pSPACES
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
• ON THE CAUCHY PROBLEM IN BESOV SPACES FOR A NON-LINEAR SCHRÖDINGER EQUATION
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the existence of infinite energy solutions for nonlinear Schrödinger equations