Algebraic bounds on the Rayleigh–Bénard attractor

Abstract The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. physical problem be equivalent one periodic and certain symmetries. This enables Gronwall estimate on enstrophy. That then used bound the L 2 norm of temperature gradient attractor, which, turn, find bounding region for enstrophy–palinstrophy plane. All final bounds are algebraic viscosity thermal diffusivity, significant improvement over previously established estimates. sharpness tested numerical simulations.