Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 269–290 | Cite as

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

  • Atanas Stefanov
  • Jiahong WuEmail author


This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where \(\Lambda - \sqrt { - \Delta } \) denotes the Zygmund operator. We establish the global existence and smoothness of classical solutions when (α, β) is in the critical range: \(\alpha > (\sqrt {1777} - 23)/24 = 0.789103...\), β > 0, and α + β = 1. This result improves previous work which obtained the global regularity for \(\alpha > (23-\sqrt {145})/12 \approx 0.9132,\;\beta>0\), and α + β = 1.


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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsOklahoma State UniversityStillwaterUSA

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