A global regularity result for the 2D Boussinesq equations with critical dissipation

2014/11/05 by Atanas Stefanov, Jiahong Wu, Stefanov, Atanas +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1411.1362

Abstract

This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by Λ^αu in the velocity equation and by Λ^βθ in the temperature equation, where Λ=√(-Δ) denotes the Zygmund operator. We establish the global existence and smoothness of classical solutions when (α,β) is in the critical range: α>(√(1777)-23)/(24) =0.798103.., β>0 and α+ β=1. This result improves the previous work of Jiu, Miao, Wu and Zhang \citeJMWZ which obtained the global regularity for α> (23-√(145))/(12) ≈ 0.9132, β>0 and α+ β=1.

Citations

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

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