Ill-Posedness for Semilinear Wave Equations with Very Low Regularity

Details Ill-Posedness for Semilinear Wave Equations with Very Low Regularity Ill-Posedness for Semilinear Wave Equations with Very Low Regularity

2007-01-28

arxiv.org/abs/math/0701794v2

Mathematische Zeitschrift, 259(2008), No. 2, 343-353

Mathematics

Analysis of PDEs

11 pages, no figures; Mathematische Zeitschrift, accepted

Scientific paper

10.1007/s00209-007-0228-y

In this paper, we study the ill-posdness of the Cauchy problem for semilinear
wave equation with very low regularity, where the nonlinear term depends on $u$
and $\partial_t u$. We prove a ill-posedness result for the "defocusing" case,
and give an alternative proof for the supercritical "focusing" case, which
improves our previous result in Chin. Ann. Math. Ser. B 26(3), 361-378, 2005.

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