The Wong-Zakai approximation and the existence of stochastic attractors for the fractional Navier-Stokes-Coriolis equation

we mainly investigate the Wong-Zakai approximation of the equation \({u}_t + \nu {( - \Delta )}^\alpha u + S{e}_3 \times u + (u \cdot \nabla )u + \nabla p = f(x,t) + h(u) \circ dW,\) besides, stochastic attractors exist. By using Euler approximation to process Brownian motion, a correlation model of fractional Navier-Stokes-Coriolis equation under approximate noise is constructed. With the help of uniform estimate and compact embedding methods, we can prove that, under the influence of approximate noise, the equation possesses stochastic attractors. On this basis, the upper semi-continuity of the stochastic attractors approximated by the equation Wong-Zakai was proved when \(\delta \to 0\).