Persistence of regularity for the viscous Boussinesq equations with zero diffusivity

Article type: Research Article

Authors: Hu, Weiwei | Kukavica, Igor^; | Ziane, Mohammed

Affiliations: Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA. E-mails: weiweihu@usc.edu, kukavica@usc.edu, ziane@usc.edu

Note: [] Corresponding author. E-mail: kukavica@usc.edu

Abstract: We address the global regularity for the 2D Boussinesq equations with positive viscosity and zero diffusivity. We prove that for data (u0,ρ0) in Hs×Hs−1, where 1<s<2, the persistence of regularity holds, i.e., the solution (u(t),ρ(t)) exists and belongs to Hs×Hs−1 for all positive t. Given the existing results, this provides the persistence of regularity for all s≥0. In addition, we address the Hs×Hs persistence and establish it for all s>1.

Keywords: Boussinesq equations, global existence, regularity, zero diffusivity, Navier–Stokes equations

DOI: 10.3233/ASY-141261

Journal: Asymptotic Analysis, vol. 91, no. 2, pp. 111-124, 2015