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On May 31, 2022 in the Dissertation Council at the Lavrentev Institute of Hydrodynamics SB RAS Dmitry A. Prokudin defended his thesis "Global existence theorems for the equations of dynamics of viscous compressible multicomponent media" for the degree of Doctor of Physics and Mathematics in the specialty 01.01.02 鈥� Differential Equations, Dynamic Systems and Optimal Control. Scientific consultant: Doctor of Sciences A. E. Mamontov.

The models of the dynamics of viscous compressible multicomponent media studied in D. A. Prokudin鈥檚 dissertation are some generalizations of the well-known system of Navier-Stokes equations for flows of a viscous compressible fluid and include the equations of continuity, impulses and energy. At the same time, the studied equations are interconnected through the leading terms by means of viscosity matrices, due to the composite structure of the tensors of viscous stresses of the components, and therefore, for their analysis, it is not enough to use the known results for the Navier-Stokes equations. For this reason, in comparison with the Navier-Stokes equations, there are not so many results for the equations of dynamics of viscous compressible multicomponent media, most of them concern either special cases (neglect of convective terms, neglect of terms in higher terms, etc.), or are local. In the thesis of D. A. Prokudin, a systematic study of the global solvability of boundary and initial-boundary value problems for the equations of dynamics of viscous compressible multicomponent media is carried out without any simplifications, and only those restrictions are imposed that express standard physical requirements.

D. A. Prokudin is a member of the research project "Differential Equations and Dynamical Systems" of the Mathematical Center in Akademgorodok.