Abstract: In recent years, a significant progress has been made through the application of the geometric and real analysis methods in some classical Leray problems on stationary motion of viscous incompressible fluid in exterior 2D domains, including the uniqueness of the solution to the problem of the plane flow around an obstacle in the class of all D-solutions, the nontriviality of the Leray solutions (obtained by the “invading domains” method) and their convergence to a given limit at low Reynolds numbers, the boundedness and the uniform convergence of D-solutions in general case, etc. A review of these advances and methods will be the focus of the talk. Most of the reviewed results were obtained in our joint articles with Konstantin Pileckas, Remigio Russo, Xiao Ren, and Julien Guillod, see, e.g., recent survey paper [1]. In the last part of the talk we consider the advances on the classical Ladyzhenskaya–Leray problem concerning the stationary fluid motion in a system of infinite channels and pipes under nonhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply-connected, and the boundary fluxes are not assumed to be small. This is a joint result with Xiao Ren (Peking University) and Filippo Gazzola, Gianmarco Sperone (Politecnico di Milano).

Cite: Korobkov M.V.
On Leray problems for steady-state Navier–Stokes system in unbounded domains
Международная конференция «Нелокальные и нелинейные задачи» 14-19 Oct 2024