题 目：Measure valued solutions and numerical schemes
报告人： Bangwei She (佘邦伟), Institute of Mathematics, Czech Academy of Sciences
摘 要: We concentrate on the question of convergence of suitable numerical schemes for viscous compressible flows. A standard paradigm for the existence of solution in fluid dynamics is based on the construction of sequences of approximate solutions or numerical schemes. However, if the underlying model does not provide enough information for the required regularity of the approximate sequence, we are facing the problem to show the convergence schemes. Inparticular, for multidimensional problems fine scale oscillations persist, which prevents us to obtain compactness result. Consequently, the standard framework of integrable functions seems not be appropriate ingeneral.
To overcome this problem we introduce the class of dissipative measure-valued solutions, which allows us to show the convergence of finite difference/volume schemes for multidimensional isentropic Navier-Stokes equations. On the other hand, using the weak-strong uniqueness result for the above systems we know, that the dissipative measure-valued solution coincides with the strong solution if the latter exists. Consequently, our results show convergence of numerical schemes to the strong solutions.
时 间：2018年7月19日 9:00-10:00
邀请人: 吕勇 老师