Attractor for the non-autonomous long wave-short wave resonance interaction equation with damping

In this paper, the long wave-short wave resonance interaction equation with a nonlinear term in bounded domain was studied. When $betageqfrac{3}{2}$, we obtained the existence and uniqueness of the weak solution of system (1.1)-(1.4) by Gal"{e}rkin''s method, and further proved the existence of the compact uniform attractor for damped driven by the non-autonomous long wave-short wave resonance interaction equation.