A controlling norm for energy-critical Schrödinger maps

2013/02/15 by Dodson, Benjamin, Smith, Paul · 1 citation
#35B33 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1302.3879

Abstract

We consider energy-critical Schroedinger maps with target either the sphere S² or hyperbolic plane H² and establish that a unique solution may be continued so long as a certain space-time L⁴ norm remains bounded. This reduces the large data global wellposedness problem to that of controlling this norm.

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• Schrödinger maps to a Kähler manifold in two dimensions

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