HIGHLIGHTS
SUMMARY
In contrast to the stability result against localized perturbations, the perturbation in Theorem 1.1 does not decay in L ∞ (R) as t → ∞, i.e. the authors do not obtain asymptotic nonlinear stability. The authors establish with the aid of Lemmas 3.11 and 3.12 Sc (t)∂ m V0 ∞ L ∞ (1 + t)- m2 ε, x (3.26) L Se (t)∂ m V0 ∞ e-μ0 t ∂ m V0 ∞ e-μ0 t W 1,∞ e-μ0 t ε, x x L L for m=0, 1 and t ∈ [0, T ). Applying the standard semigroup estimates m m . . .
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