给出了三维有旋轴对称Boussinesq方程当区域离开轴时初边值问题强解的存在唯一性.通过证明速度场u及密度▽ρ在区域离开轴时类似二维情形的L4估计,得到u,ut及ρ,ρt的先验估计,最后由Galerkin方法证得其强解的存在唯一性.由此将三维轴对称Navier--Stoke方程的相应结果推广到了三维轴对称Boussinesq方程情形.
Abstract
This paper aims at the global existence and uniqueness of strong solutions concerning the 3D axisymmetric Boussinesq equations with swirl in the region away from the symmetry axis. Based on the L4 estimation of velocity u and density ▽ρ, we obtain the prior estimates of u,ut and ρ,ρt. Finally, by Galerkin method, we obtain the global existence and uniqueness of strong solutions. In particular, this criterion extends the corresponding results of 3D axisymmetric Navier-Stoke equations to the case of 3D axisymmetric Boussinesq equations.
关键词
轴对称Boussinesq方程 /
强解 /
存在唯一性
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Key words
3D axisymmetric Boussinesq equations /
strong solutions /
existence and uniqueness
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参考文献
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