Open Mathematics (Aug 2024)

On an Oberbeck-Boussinesq model relating to the motion of a viscous fluid subject to heating

  • Iannelli Angela

DOI
https://doi.org/10.1515/math-2024-0032
Journal volume & issue
Vol. 22, no. 1
pp. 297 – 306

Abstract

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This article surveys some results in the study of Iannelli [Su un modello di Oberbeck-Boussinesq relativo al moto di un fluido viscoso soggetto a riscaldamento, Fisica Matematica, Istituto Lombardo (rend. Sc.) A 121 (1987), 145–191], in which the motion of a viscous, compressible fluid in a two-dimensional domain, subject to heating at the walls, is studied. A global existence and uniqueness theorem for the time-dependent problem is given, and also, under more stringent assumptions, an existence and uniqueness theorem in the stationary case is given. A theorem on the asymptotic behavior for t→∞t\to \infty of the time-dependent solutions is proved.

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