On the regularity properties of non-linear wave equations

S. Klainerman; Matei Machedon

Journées équations aux dérivées partielles (1997)

  • Volume: 87, Issue: 3, page 1-8
  • ISSN: 0752-0360

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Klainerman, S., and Machedon, Matei. "On the regularity properties of non-linear wave equations." Journées équations aux dérivées partielles 87.3 (1997): 1-8. <http://eudml.org/doc/93335>.

@article{Klainerman1997,
author = {Klainerman, S., Machedon, Matei},
journal = {Journées équations aux dérivées partielles},
keywords = {nonlinear wave equation; nonlocal operators; Fourier analysis techniques},
language = {eng},
number = {3},
pages = {1-8},
publisher = {Ecole polytechnique},
title = {On the regularity properties of non-linear wave equations},
url = {http://eudml.org/doc/93335},
volume = {87},
year = {1997},
}

TY - JOUR
AU - Klainerman, S.
AU - Machedon, Matei
TI - On the regularity properties of non-linear wave equations
JO - Journées équations aux dérivées partielles
PY - 1997
PB - Ecole polytechnique
VL - 87
IS - 3
SP - 1
EP - 8
LA - eng
KW - nonlinear wave equation; nonlocal operators; Fourier analysis techniques
UR - http://eudml.org/doc/93335
ER -

References

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  1. [Be] M. BealsSelf-spreading and strength of singularities for solutions to semi-linear wave equations, Annals of Math 118, 1983 no1 187-214. Zbl0522.35064MR85c:35057
  2. [B] J. BourgainFourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, I, II, Geom. Funct. Analysis 3, (1993), 107-156, 202-262. Zbl0787.35097MR95d:35160a
  3. [G] M. Grillakis, A priori estimates and regularity of non-linear waves, Proceedings of ICM, Zurich, 1994. 
  4. [Ke] M. Keel, to appear in Comm. in PDE. 
  5. [K-P-V] K. Kenig, G. Ponce, L. VegaThe Cauchy problem for the Korteveg-De Vries equation in Sobolev spaces of negative indices, Duke Math Journal 71, no 1, pp 1-21 (1994). Zbl0787.35090
  6. [K-M1] S. Klainerman and M. MachedonSpace-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math, vol XLVI, 1221-1268 (1993). Zbl0803.35095MR94h:35137
  7. [K-M2], S. Klainerman and M. MachedonOn the Maxwell-Klein-Gordon equation with finite energy, Duke Math Journal, vol. 74, no. 1 (1994). Zbl0818.35123MR95f:35210
  8. [K-M3] S. Klainerman and M. MachedonFinite energy solutions of the Yang-Mills equations in R3+1, Annals of Math. 142, 39-119 (1995). Zbl0827.53056MR96i:58167
  9. [K-M4] S. Klainerman and M. MachedonSmoothing estimates for null forms and applications, Duke Math Journal, 81, no 1, in celebration of John Nash, 99-133 (1996) Also 1994 IMRN announcement. Zbl0909.35094MR97h:35022
  10. [K-M5] S. Klainerman and M. Machedon with appendices by J. Bourgain and D. Tataru, Remark on the Strichartz inequality, International Math Research Notices no 5, 201-220 (1996). Zbl0853.35062MR97g:46037
  11. [K-M6] S. Klainerman and M. MachedonEstimates for null forms and the spaces Hs,δ International Math Research Notices no 17, 853-865 (1996). Zbl0909.35095MR98j:46028
  12. [K-M7] S. Klainerman and M. MachedonOn the regularity properties of a model problem related to wave maps, accepted, Duke Math Journal. Zbl0878.35075
  13. [K-M8] S. Klainerman and M. MachedonOn the optimal local regularity for gauge field theories, accepted, Differential and Integral Equations. Zbl0940.35011
  14. [K-S] S. Klainerman, S. SelbergRemark on the optimal regularity for equations of Wave Maps type, to appear in Comm PDE. Zbl0884.35102
  15. [K-T] S. Klainerman and D. Tataru, On the local regularity for Yang-Mills equations in R4 + 1, preprint. Zbl0924.58010
  16. [L] H. LindbladCounterexamples to local existence for semi-linear wave equations, Amer. J. Math, 118 (1996) no 1 1-16. Zbl0855.35080MR97b:35124
  17. [S] J. Shatah WeakSolutions and development of singularities for the SU (2)σ-Model, Comm. Pure Appl. Math, vol XLI 459-469 (1988). Zbl0686.35081MR89f:58044
  18. [Sch-So] W. Schlag, C SoggeLocal smoothing estimates related to the circular maximal theorem. Math Res. Letters 4 (1997) no 1-15. Zbl0877.42006MR98e:42018
  19. [So] C. SoggeOn local existence for non-linear wave equation satisfying variable coefficient null condition, Comm PDE 18 (1993) n0o 11 1795-1821. Zbl0792.35125MR94m:35199
  20. [T] D. Tataru, The Xsθ spaces and unique continuation for solutions to the semi-linear wave equation, Comm. PDE, 21 (56), 841-887 (1996). Zbl0853.35017MR97i:35012

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