Smoothing and dispersive properties of evolution equations with potential perturbations. (English) Zbl 1178.35094
Summary: We survey a group of joint results with different authors concerning the decay properties of evolution equations with variable coefficients. The problems studied include the wave, Schrödinger and Dirac equation, perturbed with electromagnetic potentials, and the main focus of the paper is on global dispersive and Strichartz estimates when the coefficients are of low regularity and of critical decay.
MSC:
35B45 | A priori estimates in context of PDEs |
35L05 | Wave equation |
58J45 | Hyperbolic equations on manifolds |
35B65 | Smoothness and regularity of solutions to PDEs |
35Q41 | Time-dependent Schrödinger equations and Dirac equations |
35B40 | Asymptotic behavior of solutions to PDEs |