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 ~ Schrodinger 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 ?' instability result Bibliography.
(source: Nielsen Book Data)
The authors consider the Schrodinger Map equation in 2 1 dimensions, with values into Sï¿½. 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?'. (source: Nielsen Book Data)