University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > About wave and Schrödinger equations in the exterior of many strictly convex obstacles

About wave and Schrödinger equations in the exterior of many strictly convex obstacles

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  • UserDavid Lafontaine, University of Bath
  • ClockMonday 18 February 2019, 15:00-16:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Ivan Moyano.

In order to study the non-linear Schrödinger and wave equations, it is crucial to understand the decay of solutions of the associated linear equations. When a trapped trajectory exists, a loss is unavoidable for a first family of a-priori estimates of the linear flow: the so-called smoothing estimates. In contrast, we will show that in the exterior of many strictly convex obstacles, the estimates of space-time norms of solutions, known as Strichartz estimates, hold with no loss with respect to the flat case, as soon as the dynamic of the trapped trajectories is sufficiently unstable. Finally, if time permits, we will say a word about the associated non-linear equations: if the geometry does not induce too much concentration of energy, we expect that the solutions behave linearly in large times.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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