Uniqueness due to noise for a dyadic model of turbulence
Seminar Room 1, Newton Institute
This research is part of the attempt to see whether the presence of noise may improve theoretical aspects of fluid dynamics, like the well posedness of certain modes. In the lecture a simple nonlinear model, called dyadic model, will be discusses. In spite of its simplicity, which allows for more detailed analysis, this model presents blow-up in regular topologies, non-uniqueness of weak solutions, anomalous energy dissipation. We show that a suitable noise restores uniqueness.