Global existence and asymptotic behavior of solutions for the Maxwell- Schrödinger equations in three space dimensions

DOI10.1007/BF02097027zbMath0766.35061OpenAlexW2003975148MaRDI QIDQ1210095

Yoshio Tsutsumi

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02097027

zbMATH Keywords

modified wave operatorCoulomb gauge condition

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Global well-posedness for the non-linear Maxwell-Schrödinger system ⋮ Global finite-energy solutions of the Maxwell-Schrödinger system ⋮ Global wellposedness in the energy space for the Maxwell-Schrödinger system ⋮ Strichartz estimates for the magnetic Schrödinger equation ⋮ Long range scattering for the Maxwell-Schrödinger system in the Lorenz gauge without any restriction on the size of data ⋮ Time global finite-energy weak solutions to the many-body Maxwell-Pauli equations ⋮ A Crank--Nicolson Finite Element Method and the Optimal Error Estimates for the Modified Time-Dependent Maxwell--Schrödinger Equations ⋮ Remarks on Non-Linear Schrödinger Equation with Magnetic Fields ⋮ Long range scattering for the Maxwell-Schrödinger system with large magnetic field data and small Schrödinger data ⋮ Global existence and uniqueness of solutions to the Maxwell-Schrödinger equations ⋮ Long range scattering for the modified Schrödinger map in two space dimensions ⋮ Scattering theory for the Schrödinger equation in some external time-dependent magnetic fields ⋮ SCATTERING THEORY FOR ZAKHAROV EQUATIONS IN THREE-DIMENSIONAL SPACE WITH LARGE DATA ⋮ Modified wave operators for the derivative nonlinear Schrödinger equation

Cites Work

• Scattering theory in the energy space for a class of nonlinear Schrödinger equations
• Existence of solutions for Schrödinger evolution equations
• On global solutions of the Maxwell-Dirac equations
• Long range scattering for nonlinear Schrödinger equations in one space dimension
• Modified wave operators for the derivative nonlinear Schrödinger equation
• Global existence of small solutions to quadratic nonlinear schrödinger equations
• The Cauchy problem for the coupled Maxwell–Schrödinger equations
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