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| On the Global Well-Posedness of 3-D Boussinesq System with Variable Viscosity |
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Citation： |
Hammadi ABIDI{,} Ping ZHANG{.On the Global Well-Posedness of 3-D Boussinesq System with Variable Viscosity[J].Chinese Annals of Mathematics B,2019,40(5):643~688 |
| Page view： 812
Net amount： 595 |
Authors： |
Hammadi ABIDI{; } Ping ZHANG{ |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11731007, 11688101) and Innovation Grant
from National Center for Mathematics and Interdisciplinary Sciences. |
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| Abstract： |
In this paper, the authors first consider the global well-posedness
of $3$-D Boussinesq system, which has variable kinematic viscosity
yet without thermal conductivity and buoyancy force, provided that
the viscosity coefficient is sufficiently close to some positive
constant in $L^\infty$ and the initial velocity is small enough in
$\dot{B}^0_{3,1}(\R^3)$. With some thermal conductivity in the
temperature equation and with linear buoyancy force $\th e_3$ on the
velo-city equation in the Boussinesq system, the authors also prove
the global well-posedness of such system with initial temperature
and initial velocity being sufficiently small in $L^1(\R^3)$ and
$\dot{B}^0_{3,1}(\R^3)$ respectively. |
Keywords： |
Boussinesq systems, Littlewood-Paley theory, Variable viscosity,Maximal regularity of heat equation |
Classification： |
35Q30, 76D03 |
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