The wave maps equation

By D. Tataru. 2004

93 citations recorded by the source corpus.

The wave maps equation has become a very popular topic in recent years. The aim of these expository notes is to present a non-technical survey of the ideas and methods which have proved useful in the study of wave maps, leading up to the latest results. The remaining open problems are also stated and explained.

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

View Paper: https://www.semanticscholar.org/paper/26034796e342cf7b7ef2807f3faa6c42fb2cb3b5

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Regularity of Wave-Maps in Dimension 2 + 1 (2009, background): “Instead, we refer the reader to the surveys [40] and [15], and the references therein.”
Strong solutions to stochastic wave equations with values in Riemannian manifolds (2007, methodology): “We refer the reader to nice surveys on geometric wave equations in [45] and [ 46 ].”
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class (2008, result): “We refer to [4], [6], [12], [13], [24], [16, Chapter 6], [10], [8] for surveys of the initial value problem for wave maps, which is of course the primary concern of this project.”
Concentration Compactness for Critical Wave Maps (2009, background): “Further, they thank Carlos Kenig, Daniel Tataru, and Jacob Sterbenz for helpful discussions.”
Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008, background): “This conjecture forms part of an intensive study of the initial value problem for the wave maps equation; see [21], [26], [49], [58], [76], [65, Chapter 6], [42], [30] for surveys of this problem.”