Abstract
The Cauchy problem for the wave equation with power type non-linearity ±∣u∣u and data in Hs+1(ℝn)×Hs(ℝn) is considered, where 0<s<(n/2)−1 and n≥3. Under the growth restriction σ*⩽4/(n−2−2s) in many cases the existence of a local solution with u(t)∈Hs+1(ℝn) is shown which is unique in a closely related class.
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