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Recently, we have given the $l^2$ bijectivity for defocusing Ablowitz-Ladiksystems in the discrete Sobolev space $l^{2,1}$ by inverse spectral method.Based on these results, the goal of this article is to investigate thelong-time asymptotic property for the initial-valued problem of the defocusingAblowitz-Ladik system with initial potential in lower regularity. The main ideais to perform proper deformations and analysis to the corespondentRiemann-Hilbert problem with the unit circle as the jump contour $\Sigma$. As aresult, we show that when $|\frac{n}{2t}|\le 1<1$, the solution admitsZakharov-Manakov type formula, and when $|\frac{n}{2t}|\ge 1>1$, the solutiondecays fast to zero.

Long-time asymptotic analysis for defocusing Ablowitz-Ladik system with initial value in lower regularity