A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations

Sergiu Klainerman

Séminaire Équations aux dérivées partielles (1999-2000)

  • Volume: 1999-2000, page 1-16

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Klainerman, Sergiu. "A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations." Séminaire Équations aux dérivées partielles 1999-2000 (1999-2000): 1-16. <http://eudml.org/doc/11005>.

@article{Klainerman1999-2000,
author = {Klainerman, Sergiu},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Minkowski space-time; basic dispersive inequality; generalized energy estimates; commuting vector fields method; Sobolev inequalities},
language = {eng},
pages = {1-16},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations},
url = {http://eudml.org/doc/11005},
volume = {1999-2000},
year = {1999-2000},
}

TY - JOUR
AU - Klainerman, Sergiu
TI - A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations
JO - Séminaire Équations aux dérivées partielles
PY - 1999-2000
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1999-2000
SP - 1
EP - 16
LA - eng
KW - Minkowski space-time; basic dispersive inequality; generalized energy estimates; commuting vector fields method; Sobolev inequalities
UR - http://eudml.org/doc/11005
ER -

References

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  1. H. Bahouri and J.Y.Chemin “Equations d’ondes quasilineaires et effect dispersif” American Journal of Mathematics 121(1999), 1337–1377. Zbl0952.35073
  2. H. Bahouri and J.Y.Chemin “Equations d’ondes quasilineaires et estimations de Strichartz” International Mathematics Research Notices 21(1999) 1141–1177. Zbl0938.35106
  3. D.Christodoulou, S.Klainerman, “Asymptotic properties of linear field equations in Minkowski space". Comm.Pure Appl.Math. XLIII,(1990), 137-199. Zbl0715.35076
  4. D.Christodoulou, S.Klainerman, “The global non linear stability of the Minkowski space". Princeton Mathematical series, 41 (1993). Zbl0827.53055
  5. L.Hormander, “Lectures on Nonlinear Hyperbolic Equations Mathematics and Applications 26, Springer-Verlag (1987). Zbl0881.35001
  6. Keel-Tao, “Endpoint Strichartz estimates”, Amer. J. Math. 120 (1998) 955-980. Zbl0922.35028
  7. S.Klainerman “Uniform decay estimates and the Lorentz invariance of the classical wave equation". Comm.Pure.Appl.Math. 38, (1985), 321-332. Zbl0635.35059
  8. S.Klainerman, “Remarks on the global Sobolev inequalities in Minkowski Space". Comm.Pure.Appl.Math. 40, (1987), 111-117. Zbl0686.46019
  9. S.Klainerman, “The null condition and global existence to nonlinear wave equations". Lect. Appl. Math. 23, (1986), 293-326. Zbl0599.35105
  10. S.Klainerman, “A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations” preprint. Zbl0993.35022
  11. S. Klainerman, I. Rodniansky “Improved regularity results for quasilinear wave equations” in preparation. 
  12. S.Klainerman, T. Sideris “On Almost Global Existence for Nonrelativistic Wave Equations in 3D” Comm.Pure.Appl.Math. 49 1996, 307-321 Zbl0867.35064
  13. O. Liess “Decay Estimates in Crystal Optics” Assymptotic Analysis 4(1991), 61-95. Zbl0735.35018
  14. C. Morawetz “The Limiting Amplitude Principle” Comm.Pure.Appl.Math. 15, 1962, 349-362. Zbl0196.41202
  15. H. Smith “A parametrix construction for wave equations with C 1 , 1 coefficients” Ann Inst Fourier de Grenoble 48(3) 1994, 797-835. Zbl0974.35068
  16. H. Smith “ Strichartz and Nullform Estimates for Metrics of Bounded Curvature” preprint. 
  17. D. Tataru “Strichartz Estimates for operators with nonsmooth coefficients and the nonlinear wave equation” To appear in AJM Zbl0959.35125
  18. D. Tataru ‘Strichartz Estimates for second order hyperbolic operators with nonsmooth coefficients III” preprint Zbl0990.35027

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