On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations

@article{Lindblad1995OnEA,
  title={On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations},
  author={Hans Lindblad and Christopher D. Sogge},
  journal={Journal of Functional Analysis},
  year={1995},
  volume={130},
  pages={357-426}
}
Abstract We prove existence and scattering results for semilinear wave equations with low regularity data. We also determine the minimal regularity that is needed to ensure local existence and well-posedness, and we give counterexamples to well-posedness. More specifically, we show that equations of the type □ u = | u | p , with initial data ( u , u t ) in Ḣ γ ( R n ) × Ḣ γ − 1 ( R n ), have a local solution if γ ≥ γ( p , n ), and we construct counterexamples if γ p , n ). The existence results… 

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