Regularity of Wave-Maps in Dimension 2 + 1

By Jacob Sterbenz, D. Tataru. 2009

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In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps $${\Phi:\mathbb{R}^{2+1} \to\mathcal{M} }$$ into general compact target manifolds $${\mathcal{M} }$$.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7ba06eea586f55638f67a70de4cf845715316eb6

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008, background): “onjecture fails [32], [43] (see also the numerical work in [1], [14]). Since the initial release of this preprint, an alternate proof of this conjecture has been provided by Sterbenz and Tataru [56], [57], as well as Krieger and Schlag (private communication). Remark 1.6. As mentioned earlier, the d”
Concentration Compactness for Critical Wave Maps (2009, background): “Further, they thank Carlos Kenig, Daniel Tataru, and Jacob Sterbenz for helpful discussions.”
Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, methodology): “The results proved here are used in the companion article [ 21 ]t o establish a full regularity theory for large data Wave-Maps.”
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009, result): “he article of Shatah and Tahvildar-Zadeh [STZ97] which established a result similar to Theorem 2 in this context, the articles of Struwe [Str02, Str03], and the recent preprint of Sterbenz and Tataru [ST09] for the general case of solutions without any special invariant properties. We also refer to ”