论文标题
关于关键Lebesgue空间中轴对称性粘性Boussinesq系统的全球良好性
On the global well-posedness of axisymmetric viscous Boussinesq system in critical Lebesgue spaces
论文作者
论文摘要
本文的贡献将集中在临界Lebesgue空间中的轴对称粘性Boussinesq系统的三维情况下的全球存在和唯一性主题。我们旨在得出最近在\ cite {gallay，gallay-sverak}中获得的经典二维和三维轴对称的纳维尔 - 斯托克斯方程的类似结果。粗略地说，我们本质上表明，如果初始数据$（v_0，ρ_0）$是轴对称的，$（ω_0，ρ_0）$属于关键空间$ l^1（ω）\ times l^1（\ MathBb {r} $ω= \ {（r，z）\ in \ mathbb {r}^2：r> 0 \} $，然后粘性boussinesq系统具有唯一的全局解决方案。
The contribution of this paper will be focused on the global existence and uniqueness topic in three-dimensional case of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. We aim at deriving analogous results for the classical two-dimensional and three-dimensional axisymmetric Navier-Stokes equations recently obtained in \cite{Gallay,Gallay-Sverak}. Roughly speaking, we show essentially that if the initial data $(v_0,ρ_0)$ is axisymmetric and $(ω_0,ρ_0)$ belongs to the critical space $L^1(Ω)\times L^1(\mathbb{R}^3)$, with $ω_0$ is the initial vorticity associated to $v_0$ and $Ω=\{(r,z)\in\mathbb{R}^2:r>0\}$, then the viscous Boussinesq system has a unique global solution.
