学术报告（赵威任 2025.9.30）

摘要：In this talk, I will first review some recent results about shear flow stability in viscous fluids. These include the stability threshold problem of shear flows in periodic channels (or in whole space) and the final behavior of solutions to the Navier-Stokes equation in the presence of Couette flow. Then, I will present recent results on three types of shear flow instabilities: 1. instability caused by perturbations (either rough or large); 2. instability induced by viscosity; and 3. instability due to boundaries. The first type of instability is related to secondary instabilities. The second type of instability typically occurs in the presence of a boundary, but I will provide an example showing that viscosity-driven instability can also occur without a boundary. The third type is the classical boundary layer instability.