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arXiv · math-ph/9912009

Dispersion and collapse of wave maps

P. Bizoń·T. Chmaj·Z. Tabor
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Abstract

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.

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P. Bizoń, T. Chmaj, Z. Tabor. 1999-12-17. Dispersion and collapse of wave maps. https://doi.org/10.1088/0951-7715%2F13%2F4%2F323

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