Academy of Mathematics and Systems Science, CAS Colloquia & Seminars | Speaker: | Associate Prof. Bangwei She,Czech Academy of Sciences | Inviter: | | Title: | Convergence of numerical solutions for the compressible Navier-Stokes system | Time & Venue: | 2021.12.09 14:30-15:30 蓝白楼311 | Abstract: | In this talk we discuss the convergence of suitable numerical schemes for the compressible viscous flows. First, we construct an energy stable scheme. Then using the a priori estimates derived from the stability, we build the consistency formulation of the scheme without any assumption on the regularity of the solution. Next, passing to the limit implies the convergence to the dissipative weak solution. Finally, using the weak-strong uniqueness principle in the class of the dissipative weak solutions, we conclude the convergence to the strong solution as long as the latter exists. These results have been obtained in collaboration with Eduard Feireisl (Czech Academy of Sciences), M\'{a}ria Luk\'a\v{c}ov\'{a} (University of Mainz), and Hana Mizerov\'{a} (Comenius University in Bratislava). | | | |