报告题目：Boundary layer associated with incompressible Newtonian flows
报 告 人：美国佛罗里达州立大学数学系主任 王晓明教授
Many physical models are simplified models that are derived by form E imensional parameters to zero. The original models can be viewed as perturbations of the limit models. These perturbations are singular in many applications in the sense that there exist singular structures in the limit. The rigorous verification of such singular limits are of physical importance in terms of model validation and in terms physical phenomena that may require the understanding of the singular structures. One well-known example is the inviscid limit of the Navier-Stokes system that governs incompressible Newtonian flows in the presence of physical walls and the associated boundary layers. The rigorous validation of the Euler system as the inviscid limit of the Navier-Stokes system is still a prominent open problem. The associated boundary layer is of great importance in fluid dynamics. In this talk, I will identify the important role played by a spectral constraint associated with appropriately constructed approximate solutions. We illustrate the application of the spectral constraint approach to several examples, including several types of flows with special symmetries, and the vanishing Darcy number limit of the Darcy-Brinkman-Oberbeck-Boussinesq system.