@article{Wang2024, 
author = {Xinli Wang and Haiyang Yu and Tianfeng Wu},
title = {Global well-posedness and optimal decay rates for the  n-D incompressible Boussinesq equations with fractional dissipation and thermal diffusion},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {34863-34885},
keywords = {fractional Boussinesq equations, fractional dissipation, thermal diffusion, optimal decay, global well-posedness},
url = {https://www.sciopen.com/article/10.3934/math.20241660},
doi = {10.3934/math.20241660},
abstract = {In this paper,  n-dimensional incompressible Boussinesq equations with fractional dissipation and thermal diffusion are investigated. Firstly, by applying frequency decomposition, we find that  ‖(u,θ)‖L2(Rn)→0, as  t→∞. Secondly, by using energy methods, we can show that if the initial data is sufficiently small in  Hs(Rn) with  s = 1+ n2−2α(0<α<1), the global solutions are derived. Furthermore, under the assumption that the initial data  (u0,  θ0) belongs to  Lp(where  1≤p<2), using a more advanced frequency decomposition method, we establish optimal decay estimates for the solutions and their higher-order derivatives. Meanwhile, the uniqueness of the system can be obtained. In the case  α = 0, we obtained the regularity and decay estimate of the damped Boussinesq equation in Besov space.}
}