Wave equation for 2D Landau Hamiltonian

TL;DR

This paper investigates the well-posedness of the wave equation associated with the 2D Landau Hamiltonian under a constant magnetic field, focusing on spectral properties and Sobolev space frameworks.

Contribution

It establishes well-posedness results for the Landau Hamiltonian wave equation in specific Sobolev spaces considering spectral characteristics.

Findings

Proves well-posedness in Sobolev spaces for the Landau Hamiltonian wave equation.

Analyzes spectral properties of the Landau Hamiltonian in the context of wave equations.

Provides a mathematical framework for understanding wave propagation under magnetic fields.

Abstract

This note is devoted to the study of the well-posedness of the Cauchy problem for the Landau Hamiltonian wave equation in the plane, with nonzero constant magnetic field. We show the well-posedness in suitably defined Sobolev spaces taking into account the spectral properties of the operator.