Mathematics Colloquia and Seminars

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Description

We prove time decay for the linearized beta-plane equation near shear flow on the plane. Specifically, we show that the profiles of the velocity field components decay polynomially on any compact set, and identify specific rates of decay. Our proof entails the analysis of oscillatory integrals with homogeneous phase and multipliers that diverge in the infinite time limit. To handle this singular limit, we prove a Van der Corput type estimate, followed by a multi-scale asymptotic analysis of the phase and multipliers. This is joint work with Jacob Bedrossian and Sameer Iyer.