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In this paper, the long wave-short wave resonance interaction equation with a nonlinear term in bounded domain was studied. When β ≥ 3 2 , we obtained the existence and uniqueness of the weak solution of system (1.1)(1.4) by Galërkin’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.

ATTRACTOR FOR THE NON-AUTONOMOUS LONG WAVE-SHORT WAVE RESONANCE INTERACTION EQUATION WITH DAMPING