Large time dynamics of 2D semi-dissipative Boussinesq equations

Abstract

Abstract In this paper, we construct an alternative proof for the long-time behavior of large-data classical solutions to the 2D semi-dissipative Boussinesq equations without thermal diffusion on a bounded domain subject to the stress-free boundary conditions, which was previously studied in Doering et al (2018 Physica D 376/7 144–59). To demonstrate the effectiveness of the new approach, we study the long-time behavior of large-data classical solutions to the initial-boundary value problem of a related model with density variance and subject to the no-flow boundary condition, for which the analytic technique utilized in Doering et al (2018 Physica D 376/7 144–59) is not directly accessible.