Abstract
We firstly proved the existence and the uniqueness of the solution for the2π-periodic fractional nonautonomous long-short wave equations with translation compact force by using Galerkin method and then obtained the compact uniform attractor of the system.
Highlights
We all know that the long-short wave resonance equations play an important role in fluid mechanics and have rich physical and mathematical properties
Guo studied the global solution for one class of the system of LS nonlinear wave interaction in [1] and the periodic initial value problems and initial value problems for one class of generalized long-short type equations in [2]
By Galerkin’s method, we construct the approximate solution of the periodic initial value problem (1)∼(4)
Summary
We consider the following fractional nonautonomous long-short wave equations with translation compact forces: iut − (−Δ)αu − nu + iδu = f (x, t) ,. Guo studied the global solution for one class of the system of LS nonlinear wave interaction in [1] and the periodic initial value problems and initial value problems for one class of generalized long-short type equations in [2]. Cui et al developed the weakly compact uniform attractor for the nonautonomous long-short wave equations with translation compact forces in [6]. Guo et al investigated the fractional nonlinear Schrodinger equation and showed the existence and uniqueness of its global smooth solution by using energy method in [14]. C(⋅, ⋅) represents the constant C expressed by the parameters appearing in the parentheses
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