On the attractor of the semi-dissipative Boussinesq equations revised

2026/07/24 by Kexin Li, Chunyou Sun
#math.AP #math.DS

paper · pdf

Abstract

In this paper, we continue investigate the structure of the weak σ-attractor A for the 2D Boussinesq equations with viscosity and without heat diffusion. Specifically, we show that the projection of the attractor A onto the temperature component is surjective, i.e., P_θA=L²; and, for any r>0, the projection of A_r onto the velocity component contains a infinite-dimensional Hilbert ellipsoid, which implies P_uA_r is infinite dimensional immediately.

Citations

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

Related

• On the Attractor for the Semi-Dissipative Boussinesq Equations
• The global attractor of the 2D Boussinesq equations with fractional Laplacian in Subcritical case
• The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity
• Strange attractors for Overbeck -Boussinesq model
• Large time behavior of solutions to a dissipative Boussinesq system