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On stationary flows of asymmetric fluids with heat convection
Author(s) -
Łukaszewicz Grzegorz,
Waluś Włodzimierz,
Piskorek A.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110304
Subject(s) - mathematics , sobolev space , uniqueness , isotropy , tensor (intrinsic definition) , convection , boundary value problem , compressibility , mathematical analysis , cauchy stress tensor , mechanics , physics , geometry , quantum mechanics
Existence, uniqueness and regularity of solutions of equations describing stationary flows of viscous incompressible isotropic fluids with an asymmetric stress tensor have been considered recently. 5 In this paper we extend the results of Reference 5 to include heat convection in the hydrodynamic model. We show that the boundary value problem (1.1)–(1.6) below has solutions in appropriate Sobolev spaces, provided the viscosities v and c a + c d are sufficiently large. The proof is based on a fixed point argument. Moreover, we show that the solutions are unique if the heat conductivity κ is large enough.