Singularity formation in 2+1 wave maps

Isenberg, James; Liebling, Steven L.

doi:10.1063/1.1418717

Singularity formation in 2+1 wave maps

Jan, 2002

6 pages

Published in:

J.Math.Phys. 43 (2002) 678-683

e-Print:

math-ph/0106029 [math-ph]

DOI:

10.1063/1.1418717

View in:

pdf

reference search5 citations

Citations per year

Abstract: (AIP)

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.

Note:

5 pages, 3 figures

References(12)

Figures(0)

[1]

On the Cauchy Problem for Harmonic maps Defined on 2 Dimensional Minkowski Space

C. Gu

- Commun.Pure Appl.Math. 33 (1980) 727-737

[2]

The Global Cauchy Problem for the Nonlinear Klein-Gordon Equations

J. Ginibre
,
G. Velo

- Math.Z. 180 (1985) 487-505

[3]

Weak Solutions and the Development of singularities in SU(2) Sigma Models

J. Shatah

- Commun.Pure Appl.Math. 41 (1988) 459-469

[4]

On the Cauchy Problem for Equivariant Wave Maps

J. Shatah
,
A.S. Tahvildar-Zadeh

- Commun.Pure Appl.Math. 47 (1994) 719-751

[5]

Classical Solutions for the Equivariant Wave Map in 1+2 Dimensions

M. Grillakis

[6]

On the Regularity of Spherically Symmetric Wave Maps

D. Christodoulou
,
A.S. Tahvildar-Zadeh

- Commun.Pure Appl.Math. 46 (1993) 1041-1051

[7]

Geometric Wave Equations, Courant Lecture Notes in Mathematics, New York University

J. Shatah
,
M. Struwe

[8]

Critical phenomena in nonlinear sigma models

- J.Math.Phys. 41 (2000) 5691-5700
•
e-Print:
- math-ph/9911020
•
DOI:
- 10.1063/1.533432

[9]

Dispersion and collapse of wave maps

P. Bizón
,
T. Chmaj
,
Z. Tabor

- Nonlinearity 13 (2000) 1411

[10]

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

P. Bizón
,
T. Chmaj
,
Z. Tabor

•
e-Print:
- math-ph/0011005

[11]

Software available from

- http://laplace.physics.ubc.ca/Members/matt/Rnpl/index.html

[12]

Universality and scaling in gravitational collapse of a massless scalar field

Matthew W. Choptuik
(
- Texas U.
)

- Phys.Rev.Lett. 70 (1993) 9-12
•
DOI:
- 10.1103/PhysRevLett.70.9