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

2020/02/28 by Hanachi, Adalet, Houamed, Haroune, Zerguine, Mohamed
#35B33 #35Q35 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.12617

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 \citeGallay,Gallay-Sverak. Roughly speaking, we show essentially that if the initial data (v₀,ρ₀) is axisymmetric and (ω₀,ρ₀) belongs to the critical space L¹(Ω)× L¹(ℝ³), with ω₀ is the initial vorticity associated to v₀ and Ω=\(r,z)∈ℝ²:r>0\, then the viscous Boussinesq system has a unique global solution.

Related

• Remarks on the global well-posedness of the axisymmetric Boussinesq system with rough initial data
• On the global solvability of the axisymmetric Boussinesq system with critical regularity
• On the global regularity of axisymmetric Navier-Stokes-Boussinesq system
• On the Global Existence for the Axisymmetric Euler-Boussinesq System in\n Critical Besov Spaces
• Global well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficient