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Counterexamples to local existence for nonlinear wave equations. (English) Zbl 0877.35081
We study how much regularity of data that is needed to ensure local existence of a solution to quasilinear wave equations. We give counterexamples to local existence for the typical model equations. The counterexamples we construct for semilinear wave equations are known to be sharp, i.e. one can prove that one has local existence if the data has slightly more regularity. The existence part has been shown in recent papers, using space time estimates know as Strichartz’ estimates or refinement of these.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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