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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1016/0300-9467(90)80046-f

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1432-0916

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Laminar Boundary Layers in Convective Heat Transpo

Authors: Christian Seis
Publish Date: 2013/10/27
Volume: 324, Issue: 3, Pages: 995-1031
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Abstract

We study Rayleigh–Bénard convection in the highRayleighnumber regime and infinitePrandtlnumber limit ie we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia effects While the dynamics in the bulk are characterized by a chaotic heat flow close to the horizontal walls the fluid is essentially motionlessWe derive local bounds on the temperature field in the boundary layers and prove that the temperature profile is essentially linear The results depend only logarithmically on the system parameters An important tool in our analysis is a new Hardytype estimate for the convecting velocity field which yields control of the fluid motion in the layer The bounds on the temperature field are derived via local maximal regularity estimates for convectiondiffusion equations

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  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
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