Strichartz Estimates for Operators with Nonsmooth Coefficients and the Nonlinear Wave Equation

Strichartz Estimates for Operators with Nonsmooth Coefficients and the Nonlinear Wave Equation

The aim of this article is threefold. First, we use the FBI transform to set up a calculus for partial differential operators with nonsmooth coefficients. Next, this calculus allows us to prove Strichartz type estimates for the wave equation with nonsmooth coefficients. Finally, we use these Stricha...

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Veröffentlicht in:American journal of mathematics 2000-04, Vol.122 (2), p.349-376
1. Verfasser: Tataru, Daniel
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Calculus
Coefficients
Commutators
Cubes
Fourier transformations
Interpolation
Mathematics
Preliminary estimates
Wave equations
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Beschreibung
Zusammenfassung:The aim of this article is threefold. First, we use the FBI transform to set up a calculus for partial differential operators with nonsmooth coefficients. Next, this calculus allows us to prove Strichartz type estimates for the wave equation with nonsmooth coefficients. Finally, we use these Strichartz estimates to improve the local theory for second order nonlinear hyperbolic equations.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2000.0014