Stable soliton resolution for equivariant wave maps exterior to a ball

Andrew Lawrie[1]

  • [1] Department of Mathematics The University of California, Berkeley 970 Evans Hall #3840 Berkeley, CA 94720 U.S.A.

Séminaire Laurent Schwartz — EDP et applications (2014-2015)

  • page 1-11
  • ISSN: 2266-0607

Abstract

top
In this report we review the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in ℝ 3 and taking values in the 3 -sphere. This is joint work with Carlos Kenig, Baoping Liu, and Wilhelm Schlag.

How to cite

top

Lawrie, Andrew. "Stable soliton resolution for equivariant wave maps exterior to a ball." Séminaire Laurent Schwartz — EDP et applications (2014-2015): 1-11. <http://eudml.org/doc/275810>.

@article{Lawrie2014-2015,
abstract = {In this report we review the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in $\mathbb\{R\}^3$ and taking values in the $3$-sphere. This is joint work with Carlos Kenig, Baoping Liu, and Wilhelm Schlag.},
affiliation = {Department of Mathematics The University of California, Berkeley 970 Evans Hall #3840 Berkeley, CA 94720 U.S.A.},
author = {Lawrie, Andrew},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {eng},
pages = {1-11},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Stable soliton resolution for equivariant wave maps exterior to a ball},
url = {http://eudml.org/doc/275810},
year = {2014-2015},
}

TY - JOUR
AU - Lawrie, Andrew
TI - Stable soliton resolution for equivariant wave maps exterior to a ball
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2014-2015
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 11
AB - In this report we review the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in $\mathbb{R}^3$ and taking values in the $3$-sphere. This is joint work with Carlos Kenig, Baoping Liu, and Wilhelm Schlag.
LA - eng
UR - http://eudml.org/doc/275810
ER -

References

top
  1. H. Bahouri and P. Gérard. High frequency approximation of solutions to critical nonlinear wave equations. Amer. J. Math., 121:131–175, 1999. Zbl0919.35089MR1705001
  2. B. Balakrishna, V. Schechter Sanyuk, J., and A. Subbaraman. Cutoff quantization and the skyrmion. Physical Review D, 45(1):344–351, 1992. 
  3. P. Bizoń, T. Chmaj, and M. Maliborski. Equivariant wave maps exterior to a ball. Nonlinearity, 25(5):1299–1309, 2012. Zbl1243.35117MR2914140
  4. T. Duyckaerts, C. Kenig, and F. Merle. Universality of the blow-up profile for small radial type II blow-up solutions of the energy critical wave equation. J. Eur math. Soc. (JEMS), 13(3):533–599, 2011. Zbl1230.35067MR2781926
  5. T. Duyckaerts, C. Kenig, and F. Merle. Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Geom. Funct. Anal., 22(3):639–698, 2012. Zbl1258.35148MR2972605
  6. T. Duyckaerts, C. Kenig, and F. Merle. Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. J. Eur. Math. Soc. (JEMS), 14(5):1389–1454, 2012. Zbl1282.35088MR2966655
  7. T. Duyckaerts, C. Kenig, and F. Merle. Classification of radial solutions of the focusing, energy critical wave equation. Cambridge Journal of Mathematics, 1(1):75–144, 2013. Zbl1308.35143MR3272053
  8. T. Duyckaerts, C. Kenig, and F. Merle. Scattering for radial, bounded solutions of focusing supercritical wave equations. To appear in I.M.R.N, Preprint, 2012. Zbl1310.35171MR3158532
  9. K. Hidano, J. Metcalfe, H. Smith, C. Sogge, and Y. Zhou. On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles. Trans. Amer. Math. Soc., 362(5):2789–2809, 2010. Zbl1193.35100MR2584618
  10. C. Kenig, A. Lawrie, B. Liu, and W. Schlag. Channels of energy for the linear radial wave equation. Preprint, 2014. Zbl1331.35209
  11. C. Kenig, A. Lawrie, B. Liu, and W. Schlag. Stable soliton resolution for exterior wave maps in all equivariance classes. Preprint, 2014. Zbl1331.35076
  12. C. Kenig, A. Lawrie, and W. Schlag. Relaxation of wave maps exterior to a ball to harmonic maps for all data. Geom. Funct. Anal., 24(2):610–647, 2014. Zbl1288.35356MR3192036
  13. C. Kenig and F. Merle. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case. Invent. Math., 166(3):645–675, 2006. Zbl1115.35125MR2257393
  14. C. Kenig and F. Merle. Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Acta Math., 201(2):147–212, 2008. Zbl1183.35202MR2461508
  15. A. Lawrie and W. Schlag. Scattering for wave maps exterior to a ball. Advances in Mathematics, 232(1):57–97, 2013. Zbl1264.35045MR2989977
  16. J. Shatah. Weak solutions and development of singularities of the SU ( 2 ) σ -model. Comm. Pure Appl. Math., 41(4):459–469, 1988. Zbl0686.35081MR933231
  17. J. Shatah and M. Struwe. Geometric wave equations. Courant Lecture notes in Mathematics, New York University, Courant Institute of Mathematical Sciences, New York. American Mathematical Society, Providence RI, 1998. Zbl1051.35500MR1674843

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.