Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions

Details Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions

2010-09-08

arxiv.org/abs/1009.1608v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the Schr\"odinger Map equation in $2+1$ dimensions, with values into $\S^2$. 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. We prove that $Q$ is unstable in the energy space $\dot H^1$. However, in the process of proving this we also show that within the equivariant class $Q$ is stable in a stronger topology $X \subset \dot H^1$.

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