Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D. (8th July 2020)

• Record Type: Journal Article
• Authors: Passerini, Arianna
• Other Names: Humi Mayer Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2020(2020)
• Publication Date: 2020-07-08
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2020/9610689
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution.