论文标题
确定性和随机3D对流Brinkman-Forchheimer方程的大量时间行为
Large time behavior of the deterministic and stochastic 3D convective Brinkman-Forchheimer equations in periodic domains
论文作者
论文摘要
确定性和随机性三维对流Brinkman-Forchheimer（CBF）方程的较大时间行为，$ r \ geq3 $（$ r> 3 $，对于任何$μ$和$β$和$ r = 3 $，而$ r = 3 $ for $2βμ\ egeq1 $），在周期性域中。我们的第一个目标是证明3D确定性CBF方程的全球吸引子的存在。然后，我们显示了3D随机CBF方程的随机吸引子的存在，这些方程式受到小添加光滑噪声的扰动。最后，当随机扰动的系数接近零时，我们为3D随机CBF方程（吸引子的稳定性）建立了随机吸引子的上半接触性（吸引子的稳定性）。
The large time behavior of the deterministic and stochastic three dimensional convective Brinkman-Forchheimer (CBF) equations for $r\geq3$ ($r>3$, for any $μ$ and $β$, and $r=3$ for $2βμ\geq1$), in periodic domains is carried out in this work. Our first goal is to prove the existence of global attractors for the 3D deterministic CBF equations. Then, we show the existence of random attractors for the 3D stochastic CBF equations perturbed by small additive smooth noise. Finally, we establish the upper semicontinuity of random attractor for the 3D stochastic CBF equations (stability of attractors), when the coefficient of random perturbation approaches to zero.
