Augmented energy method removes the p ≤ 1 + 4/(3d) restriction and proves L2 decay for attractive-dissipative NLS on data in Σ = H1 ∩ ℱH1 for the sharp range 1 < p ≤ 1 + 2/d.
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Large-data $L^2$-decay for attractive-dissipative nonlinear Schr\"odinger equations without the strong dissipative condition
Augmented energy method removes the p ≤ 1 + 4/(3d) restriction and proves L2 decay for attractive-dissipative NLS on data in Σ = H1 ∩ ℱH1 for the sharp range 1 < p ≤ 1 + 2/d.