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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2021 Volume 62, Number 5, Pages 1109–1123 (Mi smj7618)

Existence of weak solutions to the problem on three-dimensional steady heat-conductive motions of compressible viscous multicomponent mixtures

D. A. Prokudin

Voronezh State University, Voronezh, Russia

Abstract: We consider the equations describing the three-dimensional steady heat-conductive motions of compressible viscous multicomponent mixtures. We also prove the existence of weak solutions to the boundary value problem in a bounded domain without any simplifying assumptions on the structure of the viscosity matrix except for the standard physical requirement of positive definiteness.

Keywords: boundary value problem, existence theorem, dynamics of a mixture, Navier–Stokes equations, weak solution.

UDC: 517.95

MSC: 35R30

Received: 22.04.2021
Revised: 22.04.2021
Accepted: 11.06.2021

DOI: 10.33048/smzh.2021.62.512


 English version:
Siberian Mathematical Journal, 2021, 62:5, 895–907

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© Steklov Math. Inst. of RAS, 2025