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arXiv · 2002.12617

On the global well-posedness of axisymmetric viscous Boussinesq system in critical Lebesgue spaces

Adalet Hanachi·Haroune Houamed·Mohamed Zerguine
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Abstract

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 $(v_0,\rho_0)$ is axisymmetric and $(\omega_0,\rho_0)$ belongs to the critical space $L^1(\Omega)\times L^1(\mathbb{R}^3)$, with $\omega_0$ is the initial vorticity associated to $v_0$ and $\Omega=\{(r,z)\in\mathbb{R}^2:r>0\}$, then the viscous Boussinesq system has a unique global solution.

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Adalet Hanachi, Haroune Houamed, Mohamed Zerguine. 2020-02-28. On the global well-posedness of axisymmetric viscous Boussinesq system in critical Lebesgue spaces. https://arxiv.org/abs/2002.12617

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