Counterexamples to local existence for nonlinear wave equations
Journées équations aux dérivées partielles (1994), article no. 10, 5 p.
@article{JEDP_1994____A10_0,
author = {Lindblad, Hans},
title = {Counterexamples to local existence for nonlinear wave equations},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
publisher = {Ecole polytechnique},
year = {1994},
zbl = {0877.35081},
mrnumber = {95k:35136},
language = {en},
url = {http://www.numdam.org/item/JEDP_1994____A10_0}
}

Lindblad, Hans. Counterexamples to local existence for nonlinear wave equations. Journées équations aux dérivées partielles (1994), article  no. 10, 5 p. http://www.numdam.org/item/JEDP_1994____A10_0/

[1] M. Beals and M. Bezard, Low regularity local solutions for field equations, preprint. | Zbl 0852.35098

[2] L. Hörmander, The analysis of linear partial differential operators Vols. I-IV, Springer-Verlag, Berlin, 1983, 1985.

[3] S. Klainerman and M. Machedon, The null condition and local existence for nonlinear waves, Comm. Pure and Appl. Math. (to appear).

[4] H. Lindblad, A sharp counterexample to local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993), 503-539. | MR 94h:35165 | Zbl 0797.35123

[5] H. Lindblad, Counterexamples to local existence for quasilinear wave equations, in preparation (1994).

[6] H. Lindblad, Blow up for solutions of □u = |u|p with small initial data, Comm. Partial Differential Equations 15 (1990), 757-821. | MR 91k:35168 | Zbl 0712.35018

[7] H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, Jour., of Func. An (to appear). | Zbl 0846.35085

[8] G. Ponce and T. Sideris, Local regularity of nonlinear wave equations in three space dimensions, Comm. Partial Differential Equations 18 (1993), 169-177. | MR 95a:35092 | Zbl 0803.35096

[9] J. Rauch, Explosion for some Semilinear Wave Equations, Jour. of Diff. Eq. 74 (1) (1988), 29-33. | MR 89k:35022 | Zbl 0679.35068

[10] J. Shatah and A. Shadi Tahvildar-Zadeh, On the Cauchy Problem for Equivariant Wave Maps, preprint (1992). | MR 1278351

[11] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970. | MR 290095 | MR 44 #7280 | Zbl 0207.13501