Vol. 298, No. 1, 2019

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Global well-posedness for the 2D fractional Boussinesq Equations in the subcritical case

Daoguo Zhou, Zilai Li, Haifeng Shang, Jiahong Wu, Baoquan Yuan and Jiefeng Zhao

Vol. 298 (2019), No. 1, 233–255
DOI: 10.2140/pjm.2019.298.233
Abstract

We study the global regularity of solutions to the 2D Boussinesq equations with fractional dissipation, given by (Δ)α2u in the velocity equation and by (Δ)β2θ in the temperature equation. We establish the global regularity for 2 3 < α < 1, α + β > 1 and α > 1 1+β. This result is for the subcritical regime α + β > 1 and the point here is to obtain the global regularity for the largest possible range of α.

Keywords
Boussinesq equations, fractional dissipation, global regularity
Mathematical Subject Classification 2010
Primary: 35B65, 35Q35
Secondary: 76B03, 76A10
Milestones
Received: 7 March 2017
Revised: 12 January 2018
Accepted: 25 May 2018
Published: 2 February 2019
Authors
Daoguo Zhou
School of Mathematics and Information Science
Henan Polytechnic University
Henan
China
Zilai Li
School of Mathematics and Information Science
Henan Polytechnic University
Henan
China
Haifeng Shang
School of Mathematics and Information Science
Henan Polytechnic University
Henan
China
Jiahong Wu
Department of Mathematics
Oklahoma State University
Stillwater, OK
United States
Baoquan Yuan
School of Mathematics and Information Science
Henan Polytechnic University
Henan
China
Jiefeng Zhao
School of Mathematics and Information Science
Henan Polytechnic University
Henan
China