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Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions

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We consider the Schrödinger Map equation in 2 + 1 dimensions, with values into S2. 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. We prove that Q is unstable in the energy space H1. However, in the process of proving this we also show that within the equivariant class Q is stable in a stronger topology X ⊂ H 1. © 2013 by the American Mathematical Society. All rights reserved.

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