On the global well-posedness of a class of Boussinesq–Navier–Stokes systems

2009/10/02 by Changxing Miao, Liutang Xue · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35B33 #msc:35Q35 #msc:76D03 #msc:76D05

paper · pdf · doi:10.1007/s00030-011-0114-5

published as Nonlinear Differ. Equ. Appl. 18 (2011), 707-735 · 23pages

arxiv created 2009/10/02 · openalex publication_date 2011/05/09 · arxiv updated 2011/12/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems ∂_tu+u⋅∇ u+∇ p+ |D|^αu &= θe₂ ∂_tθ+u⋅∇ θ+ |D|^βθ&=0 with \textrmdiv u=0 and 0<β<α<1. When (6-√(6))/(4)<α< 1, 1-α<β≤ f(α) , where f(α) is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.

Citations

• Global regularity for the 2D Boussinesq equations with partial viscosity terms

Cited by

• On the global well-posedness of a generalized 2D Boussinesq equations

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