On Wednesday, August 2, at 16:20 in room 417 of the S. Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, the next meeting of the seminar on geometric analysis will take place. You can also connect to the seminar via Google Meet at the link
Speaker: Mikhail Korobkov (IM SB RAS, Fudan University, Shanghai)
Title of the report: On stationary solutions of the Navier-Stokes system in two-dimensional external regions: to make the long story short
Annotation:
The report is devoted to a review of results on solutions of the stationary Navier-Stokes system with a finite Dirichlet integral in an external plane domain (鈥淒-solutions鈥�). Over the past years, some progress has been achieved in this problem: uniform boundedness in the C-norm and uniform convergence (at spatial infinity) of such solutions, unique solution to the problem of flow around an obstacle in the class of all D-solutions, non-triviality of Leray solutions (obtained by the 鈥渄omain invasion鈥� method) ) in the problem of flow around an obstacle and their convergence to a given lim it at low Reynolds numbers.
Quite recently it turned out that all the mentioned results can be easily derived from some basic estimates for general Navier鈥揝tokes solutions. These estimates have a fairly simple form and control the difference in the average speed values along two concentric circles through the Dirichlet integral in the ring between them. Most of the results discussed were obtained in our joint work with Konstantin Pileckas, Remigio Russo, Xiao Ren, and Julien Guillod, see also the recent review article by J. Math. Fluid Mech., Vol.25 (55) (2023),
