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Counterexamples to local existence for semi-linear wave equations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 118, Number 1, February 1996
- pp. 1-16
- 10.1353/ajm.1996.0002
- Article
- Additional Information
In this paper we study how much regularity of initial data is needed to ensure existence of a local solution to a semi-linear wave equation. We give counterexamples to local existence for the typical model equations. The counterexamples we construct are sharp, i.e. one does have a local solution if the data has slightly more regularity.