Global existence for Schrödinger–Debye system for initial data with infinite 𝐿²-norm

DOI10.1090/S0033-569X-2015-01371-4zbMath1318.35104OpenAlexW2962921683MaRDI QIDQ5254370

Lucas C. F. Ferreira, Adán J. Corcho

Publication date: 9 June 2015

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0033-569x-2015-01371-4

zbMATH Keywords

asymptotic stabilityglobal existencesingular dataSchrödinger-Debye system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Existence and scattering theory for Boussinesq type equations with singular data
• Sharp bilinear estimates and well posedness for the 1-D Schrödinger-Debye system.
• On the periodic Schrödinger-Deybe equation
• Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
• On the Cauchy problem for some systems occurring in nonlinear optics
• On the nonstationary Navier-Stokes systems
• Local and global well-posedness for the critical Schrödinger-Debye system
• On the existence of infinite energy solutions for nonlinear Schrödinger equations
• THE CAUCHY PROBLEM FOR SCHRÖDINGER–DEBYE EQUATIONS
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