Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions

ISBN-13: 9780821892152 / Angielski

Ioan Bejenaru;Daniel Tataru

Opis

The authors consider the Schrodinger Map equation in 2+1 dimensions, with values into Si 1/2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space ?'. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology XC?'."

Spis treści

• Introduction
• An outline of the paper
• The Coulomb gauge representation of the equation
• Spectral analysis for the operators H, H ~ ; the X,LX spaces
• The linear H ~ Schrödinger equation
• The time dependent linear evolution
• Analysis of the gauge elements in X,LX
• The nonlinear equation for ?
• The bootstrap estimate for the ? parameter
• The bootstrap argument
• The ?¹ instability result
• Bibliography