Abstract
We continue our study of the three-dimensional initial boundary-value problem of the convection of a viscous thermally inhomogeneous weakly compressible fluid which fills a cavity in a solid body. We prove theorems on the uniqueness of the generalized solution of this problem and its continuity with respect to initial conditions and perturbations. We obtain estimates of exponential type for the decay of solutions (in the mean) for large time.
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V. B. Moseenkov, “Three-dimensional initial boundary-value problem of the convection of a viscous weakly compressible fluid. I. Global solvability,”Ukr. Mat. Zh.,46, No. 5, 524–536 (1994).
V. B. Moseenkov, “Axially symmetric initial boundary-value problem of the convection of a viscous weakly compressible fluid. I. Unique global solvability”,Ukr. Mat. Zh.,42, No. 12, 1664–1672 (1990).
V. B. Moseenkov, “Axially symmetric initial boundary-value problem of the convection of a viscous weakly compressible fluid. II. Stability of generalized solutions,”Ukr. Mat. Zh.,43, No. 1, 99–105 (1991).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1189–1202, September, 1994.
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Moseenkov, V.B. Three-dimensional initial boundary-value problem of the convection of a viscous weakly compressible fluid. II. Uniqueness and stability of generalized solutions. Ukr Math J 46, 1307–1321 (1994). https://doi.org/10.1007/BF01059421
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DOI: https://doi.org/10.1007/BF01059421