## Aims

[Updated, August 29, 2012]

Things to work:

1. [In progress] Pullback attractors for E-E Davey-Stewartson systems on $\mathbb R^2$

$\begin{cases} iu_t + \Delta u + \lambda u = a|u|^2u + bu\varphi_x + g(t,x)\\ \Delta \varphi = \partial_x(|u|^2)\end{cases}$.

2. [Change title and new organization] Regularity of pullback attractors for stochastic reaction diffusion equations on unbounded domains.

$u_t - \Delta u + f(x,u) + \lambda u = g(t,x) + hd\omega$.

3. [Submitted] Random attractors for stochastic 3D Navier-Stokes-Voight equations on unbounded domains and upper semi-continuity.

$u_t - \alpha\Delta u_t - \nu\Delta u + \nabla p + u\cdot \nabla u +\lambda u= g(x) + \epsilon h d \omega$.

New goals:

1. Existence and upper semi-continuity of pullback attractors for regularized Navier-Stokes equations on unbounded domains

$u_t - \varepsilon\Delta^2 u - \nu\Delta u + \nabla p + u\cdot \nabla u +\lambda u= g(t)$.

2. Random attractors for reaction diffusion equations with dynamical boundary conditions on unbounded domains

$u_t -\Delta u + f(u)= g(t,x) + hd\omega, x\in\Omega, t>0$.

$u_t - \dfrac{\partial u}{\partial \nu} + h(u) = \rho(t), x\in\partial\Omega,t>0$.