Manli Song

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math.AP2026

Decay estimates for a class of dispersive equations with partial inverse-square potentials

Jiabin Qian, Manli Song

Let $L_{a} = - I^_{x} - I^_{y} + \frac{a}{2} ∣ x ∣^{- 2}$ with $a > 0$ denote the SchrÃ¶dinger operator on $L^{2} (R_{x}^{2} \times R_{y}^{n})$ , which involves a singular partial inve…

math.AP2026

Dispersive decay for the mass-critical SchÃ¶dinger equation when $d \geq 3$

Jiabin Qian, Manli Song

In this paper we establish the pointwise-in-time dispersive decay for solutions to the mass-critical nonlinear SchrÃ¶dinger equation in spatial dimensions $d \geq 3$ . Our argument re…

Decay estimates for a class of dispersive equations with partial inverse-square potentials

Dispersive decay for the mass-critical SchÃ¶dinger equation when d≥3

Dispersive decay for the mass-critical SchÃ¶dinger equation when $d \geq 3$