A controlling norm for energy-critical Schrödinger maps

Dodson, Benjamin; Smith, Paul

doi:10.1090/S0002-9947-2015-06417-4

A controlling norm for energy-critical Schrödinger maps
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by Benjamin Dodson and Paul Smith PDF

Trans. Amer. Math. Soc. 367 (2015), 7193-7220 Request permission

Abstract:

We consider energy-critical Schrödinger maps with target either the sphere $\mathbb {S}^2$ or hyperbolic plane $\mathbb {H}^2$ and establish that a unique solution may be continued so long as a certain space-time $L^4$ norm remains bounded. This reduces the large data global wellposedness problem to that of controlling this norm.

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