Weighted Strichartz estimates and global existence for semilinear wave equations
Authors:
- Vladimir GeorgievVGVladimir Georgiev
- Hans LindbladHLHans Lindblad
- Christopher D. SoggeCSChristopher D. Sogge
- 1 December 1997
- journal article
- research article
- Published by Project MUSE in American Journal of Mathematics
- Vol. 119 (6) , 1291-1319
Abstract
In this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power-type nonlinearities. The proof is based on a weighted Strichartz estimate involving powers of the Lorentz distance.Keywords
This publication has 12 references indexed in Scilit:
- Long-time existence for small amplitude semilinear wave equationsAmerican Journal of Mathematics, 1996
- On Existence and Scattering with Minimal Regularity for Semilinear Wave EquationsJournal of Functional Analysis, 1995
- Propagation of singularities and maximal functions in the planeInventiones Mathematicae, 1991
- Regularity Properties of Fourier Integral OperatorsAnnals of Mathematics, 1991
- Finite-time blow-up for nonlinear wave equations in high dimensionsCommunications in Partial Differential Equations, 1987
- Nonexistence of global solutions to semilinear wave equations in high dimensionsJournal of Differential Equations, 1984
- Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equationsDuke Mathematical Journal, 1977
- Space-time decay for solutions of wave equationsAdvances in Mathematics, 1976
- A priori estimates for the wave equation and some applicationsJournal of Functional Analysis, 1970
- Interpolation of linear operatorsTransactions of the American Mathematical Society, 1956