6 papers · 1 filter
Almost global existence for quasilinear wave equations in three space dimensions
M. Keel, H. Smith, C. D. Sogge
We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski sp…
Almost global existence for some semilinear wave equations
Markus Keel, Hart Smith, Christopher D. Sogge
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euc…
Global existence for a quasilinear wave equation outside of star-shaped domains
Markus Keel, Hart Smith, Christopher Sogge
We establish global existence in 3+1 dimensions of small-amplitude solutions of quasilinear Dirichlet-wave equations satisfying the null condition outside of star-shapped obstacles…
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…
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…