Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class

By Terence Tao. 2008

53 citations recorded by the source corpus.

Using the harmonic map heat flow, we construct an energy class for wave maps $\phi$ from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$, and then show (conditionally on a large data well-posedness claim for such wave maps) that no stationary, travelling, self-similar, or degenerate wave maps exist in this energy class. These results form three of the five claims required in our earlier paper (arXiv:0805.4666) to prove global regularity for such wave maps. (The conditional claim of large data well-posedness is one of the remaining claims required in that paper.)

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2509a25a1755f1c96dd3efba8d7489081732354d

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In Applied Mathematics

1. Jacob Sterbenz
2. D. Tataru
3. Terence Tao
4. Carlos E. Kenig
5. Zihua Guo
6. J. Krieger
7. A. Ionescu
8. Wilhelm Schlag

In Mathematical Physics

1. Jacob Sterbenz
2. D. Tataru
3. Terence Tao
4. Carlos E. Kenig
5. A. Ionescu
6. J. Krieger
7. Zihua Guo
8. Luc Molinet

Citations in the corpus

• Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, background): “In the case where M = Hn , the hyperbolic spaces, global regularity and scattering follows from the program of Tao [22–24,26,30] and [25].”
• Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008, background): “Then there exists a normalised ancient solution with non-zero energy.”