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Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation
Hart Smith, Christopher D. Sogge
The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman…
Averages over curves with torsion
Daniel Oberlin, Hart Smith, Christopher D. Sogge
We establish Sobolev mapping properties for averages over certain curves in , which improve upon the estimates obtained by interpolation.
Global Strichartz estimates for nontrapping perturbations of the Laplacian
Hart Smith, Christopher D. Sogge
The authors prove global Strichartz estimates for compact perturbations of the wave operator in odd dimensions when a non-trapping assumption is satisfied.
On Global existence for nonlinear wave equations outside of convex obstacles
Marcus Keel, Hart Smith, Christopher D. Sogge
We prove global existence for semilinear hyperbolic equations that satisfy the null condition of Christodoulou and Klainerman in the exterior of convex domains. We use a combinatio…