Global Parametrices and Dispersive Estimates for Variable Coefficient Wave Equations
نویسندگان
چکیده
In this article we consider variable coefficient time dependent wave equations in R×R. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C metrics which satisfy a weak asymptotic flatness condition at infinity.
منابع مشابه
Parametrices and Dispersive Estimates for Schroedinger Operators with Variable Coefficients
In this article we consider variable coefficient time dependent Schrödinger evolutions in R. For this we use phase space methods to construct outgoing parametrices and to prove global in time Strichartz type estimates. This is done in the context of C metrics which satisfy a weak asymptotic flatness condition at infinity.
متن کاملNull Form Estimates for (1/2,1/2) Symbols and Local Existence for a Quasilinear Dirichlet-wave Equation
We establish certain null form estimates of Klainerman-Machedon for parametrices of variable coefficient wave equations for the convex obstacle problem, and for wave equations with metrics of bounded curvature. These are then used to prove a local existence theorem for nonlinear Dirichlet-wave equations outside of convex obstacles.
متن کاملLocal and global analysis of nonlinear dispersive and wave equations
Contents Preface ix Chapter 1. Ordinary differential equations 1 1.1. General theory 1 1.2. Gronwall's inequality 7 1.3. Bootstrap and continuity arguments 14 1.4. Noether's theorem 18 1.5. Monotonicity formulae 25 1.6. Linear and semilinear equations 28 1.7. Completely integrable systems 35 Chapter 2. Constant coefficient linear dispersive equations 41 2.1. The Fourier transform 47 2.2. Fundam...
متن کاملSmoothing Properties of Evolution Equations via Canonical Transforms and Comparison
The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov–type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...
متن کاملSmoothing Estimates for Evolution Equations via Canonical Transforms and Comparison
The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...
متن کامل