Random attractors for 2D stochastic convective Brinkman-Forchheimer equations in some unbounded domains
Kush Kinra, Manil T. Mohan · arXiv (Cornell University) · 2020
In this paper, we consider the two-dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations in unbounded domains like Poincare domains and discuss about the asymptotic behavior of its solution. We establish the existence of random attractors for the stochastic flow generated by the 2D SCBF equations with additive rough noise on Poincare domains. One of the technical difficulties connected with the rough noise is overcame with the help of the corresponding Cameron-Martin space (or Reproducing Kernel Hilbert space). Furthermore, we observe that the regularity of the rough noise needed to obtain random attractors for the 2D SCBF equations for $r \in [1,3]$ is same as that in the case of 2D Navier-Stokes equations, where as for the case $r\in (3, \infty)$, we require more spatial regularity on the noise.