Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

Details Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

2000-11-02

arxiv.org/abs/math-ph/0011005v2

Physics

Mathematical Physics

14 pages, 5 figures, final version to be published in Nonlinearity

Scientific paper

10.1088/0951-7715/14/5/308

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.

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