Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions

2010/09/08 by Bejenaru, Ioan, Tataru, Daniel · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1009.1608

Abstract

We consider the Schrödinger Map equation in 2+1 dimensions, with values into §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 H¹. However, in the process of proving this we also show that within the equivariant class Q is stable in a stronger topology X ⊂ H¹.

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