Counterexamples to local existence for nonlinear wave equations

Hans Lindblad

Journées équations aux dérivées partielles (1994)

  • Volume: 1994, page 1-5
  • ISSN: 0752-0360

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Lindblad, Hans. "Counterexamples to local existence for nonlinear wave equations." Journées équations aux dérivées partielles 1994 (1994): 1-5. <http://eudml.org/doc/93278>.

@article{Lindblad1994,
author = {Lindblad, Hans},
journal = {Journées équations aux dérivées partielles},
keywords = {quasilinear wave equations; Strichartz' estimates},
language = {eng},
pages = {1-5},
publisher = {Ecole polytechnique},
title = {Counterexamples to local existence for nonlinear wave equations},
url = {http://eudml.org/doc/93278},
volume = {1994},
year = {1994},
}

TY - JOUR
AU - Lindblad, Hans
TI - Counterexamples to local existence for nonlinear wave equations
JO - Journées équations aux dérivées partielles
PY - 1994
PB - Ecole polytechnique
VL - 1994
SP - 1
EP - 5
LA - eng
KW - quasilinear wave equations; Strichartz' estimates
UR - http://eudml.org/doc/93278
ER -

References

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  1. [1] M. Beals and M. Bezard, Low regularity local solutions for field equations, preprint. Zbl0852.35098
  2. [2] L. Hörmander, The analysis of linear partial differential operators Vols. I-IV, Springer-Verlag, Berlin, 1983, 1985. Zbl0521.35001
  3. [3] S. Klainerman and M. Machedon, The null condition and local existence for nonlinear waves, Comm. Pure and Appl. Math. (to appear). Zbl0803.35095
  4. [4] H. Lindblad, A sharp counterexample to local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993), 503-539. Zbl0797.35123MR94h:35165
  5. [5] H. Lindblad, Counterexamples to local existence for quasilinear wave equations, in preparation (1994). Zbl0877.35081
  6. [6] H. Lindblad, Blow up for solutions of □u = |u|p with small initial data, Comm. Partial Differential Equations 15 (1990), 757-821. Zbl0712.35018MR91k:35168
  7. [7] H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, Jour., of Func. An (to appear). Zbl0846.35085
  8. [8] G. Ponce and T. Sideris, Local regularity of nonlinear wave equations in three space dimensions, Comm. Partial Differential Equations 18 (1993), 169-177. Zbl0803.35096MR95a:35092
  9. [9] J. Rauch, Explosion for some Semilinear Wave Equations, Jour. of Diff. Eq. 74 (1) (1988), 29-33. Zbl0679.35068MR89k:35022
  10. [10] J. Shatah and A. Shadi Tahvildar-Zadeh, On the Cauchy Problem for Equivariant Wave Maps, preprint (1992). 
  11. [11] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970. Zbl0207.13501MR44 #7280

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