The HADES seminar on Tuesday, February 10th, will be at 3:30PM on Zoom.

Speaker: Yongming Li

Abstract: In this talk we present a perturbative proof of the asymptotic stability of the solitary wave solutions for the 1D focusing cubic Schrödinger equation under small perturbations in weighted Sobolev spaces. The strategy of our proof is based on the space-time resonances approach, using the distorted Fourier transform and modulation techniques to capture the asymptotic behavior of the solution. A major difficulty throughout the nonlinear analysis is the slow local decay of the radiation term caused by the threshold resonances in the spectrum of the linearized operator around the solitary wave. The presence of favorable null structures in the quadratic terms mitigates this problem through the use of normal form transformations.

The HADES seminar on Tuesday, February 3rd, will be at 3:30pm in Room 740.

Speaker: Felix Brandt

Abstract: The CAO-problem concerns a system of two fluids described by two primitive equations coupled by nonlinear interface conditions. Lions, Temam and Wang proved in their pioneering work the existence of a weak solution to the CAO-system. Its uniqueness remained an open problem.

In this talk, we show that this coupled CAO-system is globally strongly well-posed for large data in critical Besov spaces. The approach presented relies on an optimal data result for the boundary terms in the linearized system in terms of time-space Triebel-Lizorkin spaces. Boundary terms are controlled by paraproduct methods.

This talk is based on joint work with Tim Binz, Matthias Hieber and Tarek Zöchling.