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On the characteristic curvature operator
Global well-posedness and scattering for Skyrme wave maps
1. | Department of Mathematics, University of Rochester, Rochester, NY 14627, United States |
2. | Department of Mathematics, Kyoto University, Kyoto 606-8502 |
3. | Department of Physics and Astronomy, Department of Mathematics, University of Rochester, Rochester, NY 14627, United States |
References:
[1] |
G. Adkins and C. Nappi, Stabilization of chiral solitons via vector mesons, Phys. Lett. B, 137 (1984), 251-256.
doi: 10.1016/0370-2693(84)90239-9. |
[2] |
P. Bizoń, T. Chmaj and A. Rostworowski, Asymptotic stability of the skyrmion, Phys. Rev. D, 75 (2007), 121702-121706.
doi: 10.1103/PhysRevD.75.121702. |
[3] |
D.-A. Geba and S. G. Rajeev, A continuity argument for a semilinear Skyrme model, Electron. J. Differential Equations, 2010 (2010), 1-9. |
[4] |
D.-A. Geba and S. G. Rajeev, Nonconcentration of energy for a semilinear Skyrme model, Ann. Physics, 325 (2010), 2697-2706.
doi: 10.1016/j.aop.2010.07.002. |
[5] |
D.-A. Geba and S. G. Rajeev, Energy arguments for the Skyrme model, work in progress. |
[6] |
D.-A. Geba and D. da Silva, On the regularity of the $2+1$ dimensional Skyrme model, preprint, arXiv:1106.3974. |
[7] |
M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cimento, 16 (1960), 705-726.
doi: 10.1007/BF02859738. |
[8] |
F. Gürsey, On the symmetries of strong and weak interactions, Nuovo Cimento, 16 (1960), 230-240.
doi: 10.1007/BF02860276. |
[9] |
F. Gürsey, On the structure and parity of weak interaction currents, Ann. Physics, 12 (1961), 91-117.
doi: 10.1016/0003-4916(61)90147-6. |
[10] |
D. Li, Global wellposedness of hedgehog solutions for the ($3+1$) Skyrme model, preprint, 2011. |
[11] |
F. Lin and Y. Yang, Analysis on Faddeev knots and Skyrme solitons: recent progress and open problems, Perspectives in nonlinear partial differential equations, Contemp. Math., 446 (2007), 319-344.
doi: 10.1090/conm/446/08639. |
[12] |
J. Shatah, Weak solutions and development of singularities of the SU(2) $\sigma$-model, Comm. Pure Appl. Math., 41 (1988), 459-469.
doi: 10.1002/cpa.3160410405. |
[13] |
T. H. R. Skyrme, A non-linear field theory, Proc. Roy. Soc. London Ser. A, 260 (1961), 127-138.
doi: 10.1098/rspa.1961.0018. |
[14] |
T. H. R. Skyrme, Particle states of a quantized meson field, Proc. Roy. Soc. London Ser. A, 262 (1961), 237-245.
doi: 10.1098/rspa.1961.0115. |
[15] |
T. H. R. Skyrme, A unified field theory of mesons and baryons, Nuclear Phys., 31 (1962), 556-569.
doi: 10.1016/0029-5582(62)90775-7. |
[16] |
D. Tataru, Local and global results for wave maps I, Comm. Partial Differential Equations, 23 (1998), 1781-1793.
doi: 10.1080/03605309808821400. |
[17] |
N. Turok and D. Spergel, Global texture and the microwave background, Phys. Rev. Lett., 64 (1990), 2736-2739.
doi: 10.1103/PhysRevLett.64.2736. |
show all references
References:
[1] |
G. Adkins and C. Nappi, Stabilization of chiral solitons via vector mesons, Phys. Lett. B, 137 (1984), 251-256.
doi: 10.1016/0370-2693(84)90239-9. |
[2] |
P. Bizoń, T. Chmaj and A. Rostworowski, Asymptotic stability of the skyrmion, Phys. Rev. D, 75 (2007), 121702-121706.
doi: 10.1103/PhysRevD.75.121702. |
[3] |
D.-A. Geba and S. G. Rajeev, A continuity argument for a semilinear Skyrme model, Electron. J. Differential Equations, 2010 (2010), 1-9. |
[4] |
D.-A. Geba and S. G. Rajeev, Nonconcentration of energy for a semilinear Skyrme model, Ann. Physics, 325 (2010), 2697-2706.
doi: 10.1016/j.aop.2010.07.002. |
[5] |
D.-A. Geba and S. G. Rajeev, Energy arguments for the Skyrme model, work in progress. |
[6] |
D.-A. Geba and D. da Silva, On the regularity of the $2+1$ dimensional Skyrme model, preprint, arXiv:1106.3974. |
[7] |
M. Gell-Mann and M. Lévy, The axial vector current in beta decay, Nuovo Cimento, 16 (1960), 705-726.
doi: 10.1007/BF02859738. |
[8] |
F. Gürsey, On the symmetries of strong and weak interactions, Nuovo Cimento, 16 (1960), 230-240.
doi: 10.1007/BF02860276. |
[9] |
F. Gürsey, On the structure and parity of weak interaction currents, Ann. Physics, 12 (1961), 91-117.
doi: 10.1016/0003-4916(61)90147-6. |
[10] |
D. Li, Global wellposedness of hedgehog solutions for the ($3+1$) Skyrme model, preprint, 2011. |
[11] |
F. Lin and Y. Yang, Analysis on Faddeev knots and Skyrme solitons: recent progress and open problems, Perspectives in nonlinear partial differential equations, Contemp. Math., 446 (2007), 319-344.
doi: 10.1090/conm/446/08639. |
[12] |
J. Shatah, Weak solutions and development of singularities of the SU(2) $\sigma$-model, Comm. Pure Appl. Math., 41 (1988), 459-469.
doi: 10.1002/cpa.3160410405. |
[13] |
T. H. R. Skyrme, A non-linear field theory, Proc. Roy. Soc. London Ser. A, 260 (1961), 127-138.
doi: 10.1098/rspa.1961.0018. |
[14] |
T. H. R. Skyrme, Particle states of a quantized meson field, Proc. Roy. Soc. London Ser. A, 262 (1961), 237-245.
doi: 10.1098/rspa.1961.0115. |
[15] |
T. H. R. Skyrme, A unified field theory of mesons and baryons, Nuclear Phys., 31 (1962), 556-569.
doi: 10.1016/0029-5582(62)90775-7. |
[16] |
D. Tataru, Local and global results for wave maps I, Comm. Partial Differential Equations, 23 (1998), 1781-1793.
doi: 10.1080/03605309808821400. |
[17] |
N. Turok and D. Spergel, Global texture and the microwave background, Phys. Rev. Lett., 64 (1990), 2736-2739.
doi: 10.1103/PhysRevLett.64.2736. |
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