Concentration-diffusion phenomena of heat convection in an incompressible fluid

Reinhard Farwig; Raphael Schulz; Masao Yamazaki

doi:10.3233/ASY-131211

Concentration-diffusion phenomena of heat convection in an incompressible fluid

Reinhard Farwig^*, Raphael Schulz, Masao Yamazaki

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study in the whole space Rⁿ the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L^∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration-diffusion phenomenon.

Original language	English
Pages (from-to)	17-41
Number of pages	25
Journal	Asymptotic Analysis
Volume	88
Issue number	1-2
DOIs	https://doi.org/10.3233/ASY-131211
Publication status	Published - 2014

Keywords

concentration-diffusion
instationary Boussinesq equations
mild and strong solutions
rate of decay in space
weighted spaces

ASJC Scopus subject areas

General Mathematics

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abstract = "We study in the whole space Rn the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration-diffusion phenomenon.",

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AU - Farwig, Reinhard

AU - Schulz, Raphael

AU - Yamazaki, Masao

PY - 2014

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N2 - We study in the whole space Rn the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration-diffusion phenomenon.

AB - We study in the whole space Rn the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration-diffusion phenomenon.

KW - concentration-diffusion

KW - instationary Boussinesq equations

KW - mild and strong solutions

KW - rate of decay in space

KW - weighted spaces

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ER -

Concentration-diffusion phenomena of heat convection in an incompressible fluid

Abstract

Keywords

ASJC Scopus subject areas

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