scholarly journals Existence and nonlinear stability of convective solutions for almost compressible fluids in Bénard problem

2019 ◽  
Vol 60 (11) ◽  
pp. 113101 ◽  
Author(s):  
Antonino De Martino ◽  
Arianna Passerini
Keyword(s):  
Nonlinear Stability ◽  
Compressible Fluids ◽  
Bénard Problem ◽  
Benard Problem

scholarly journals Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Arianna Passerini
Keyword(s):  
Pressure Field ◽  
Fluid Model ◽  
Classical Model ◽  
Compressible Fluids ◽  
Heat Conducting ◽  
Regular Solutions ◽  
New Approach ◽  
Slightly Compressible ◽  
Bénard Problem ◽  
Benard Problem

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.

A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem

1985 ◽  
Vol 402 (1823) ◽  
pp. 257-283 ◽  
Keyword(s):  
Prandtl Number ◽  
Nonlinear Analysis ◽  
Nonlinear Stability ◽  
Close Agreement ◽  
Stability Boundary ◽  
Stabilizing Effect ◽  
Bénard Problem ◽  
Benard Problem

This paper uses a novel ‘generalized energy’ to study the stabilizing effect of rotation in the Bénard problem. The nonlinear stability boundary we find is in very close agreement with the experiments of Rossby (Rossby, H. T. J . Fluid Mech . 36, 309–335 (1969)), who predicts sub-critical instabilities for high Taylor numbers for fluids with Prandtl number greater than or equal to 1, such as water.

Nonlinear stability of the viscoelastic Bénard problem

Nonlinearity ◽  
2020 ◽  
Vol 33 (4) ◽  
pp. 1677-1704
Author(s):  
Fei Jiang ◽  
Mengmeng Liu
Keyword(s):  
Nonlinear Stability ◽  
Bénard Problem ◽  
Benard Problem
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