On the global well-posedness of axisymmetric viscous Boussinesq system in critical Lebesgue spaces
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
