Ill-Posedness for Semilinear Wave Equations with Very Low Regularity

Abstract

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.

11 pages, no figures; Mathematische Zeitschrift, accepted

References in corpus (2)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Sharp Global Existence for Semilinear Wave Equation with Small Data

Cited by in corpus (4)

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• Sharp Global Existence for Semilinear Wave Equation with Small Data
• Global Regularity for Supercritical Nonlinear Dissipative Wave Equations in 3D