Global Existence and Uniqueness of Solutions to the Maxwell-Schr{ö}dinger Equations

Abstract

The time local and global well-posedness for the Maxwell-Schr{ö}dinger equations is considered in Sobolev spaces in three spatial dimensions. The Strichartz estimates of Koch and Tzvetkov type are used for obtaining the solutions in the Sobolev spaces of low regularities. One of the main results is that the solutions exist time globally for large data.

arXiv comment30 pages. In the revised version, the following modification was made. (1) A line for dedication was added in the first page. (2) Some lines were added at the bottom in page 4 and the top in page 5 in the first section to make the description accurate. (3) Some typographical errors were corrected throughout the paper

References in corpus (1)

• Long Range Scattering and Modified Wave Operators for the Maxwell-Schr"odinger system I.The case of vanishing asymptotic magnetic field

Cited by in corpus (6)

• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials
• Existence of a Unique Local Solution to the Many-body Maxwell-Schrödinger Initial Value Problem
• Time Global Finite-Energy Weak Solutions to the Many-Body Maxwell-Pauli Equations
• Lectures on Quantum Mechanics for mathematicians
• The Maxwell-Pauli Equations