Yongming Luo

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20232026

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math.AP2026

Unconditional uniqueness for the cubic nonlinear Schrödinger equation in $H ˙^{\frac{1}{2}} (R^{3})$

Yongming Luo, Jiayu Zheng

While unconditional uniqueness for the cubic nonlinear Schrödinger equation (NLS) on $R^{3}$ is known in the scaling-subcritical Sobolev spaces $H ˙^{s} (R^{3})$ for $1/2<s<1…

math.AP2026

Almost sure local well-posedness for the nonlinear Schrödinger equations on $T^{d}$ with non-algebraic nonlinearity

Yongming Luo

We study the Cauchy problem for the nonlinear Schrödinger equation on $T^{d}$ with random initial data and a general non-algebraic power-type nonlinearity. We establish almos…

math.AP2026

Sharp mass-threshold for Dancer-type solutions of the focusing mass-critical NLS on $R^{d} \times T$

Yongming Luo

The mass-critical NLS on Euclidean space $R^{d}$ exhibits a strong mass rigidity: all positive ground states are generated from a single profile and have the same ground state mass…

math.AP2026

On Dancer-type solutions for the Lane--Emden equation via semivirial-vanishing geometry

Yongming Luo

Aubin--Talenti bubbles describe the decaying positive solutions of the zero-frequency critical Lane--Emden equation in Euclidean space. By appealing to bifurcation methods, Dancer…

Unconditional uniqueness for the cubic nonlinear Schrödinger equation in H˙21​(R3)

Almost sure local well-posedness for the nonlinear Schrödinger equations on Td with non-algebraic nonlinearity

Sharp mass-threshold for Dancer-type solutions of the focusing mass-critical NLS on Rd×T

On Dancer-type solutions for the Lane--Emden equation via semivirial-vanishing geometry

Unconditional uniqueness for the cubic nonlinear Schrödinger equation in $H ˙^{\frac{1}{2}} (R^{3})$

Almost sure local well-posedness for the nonlinear Schrödinger equations on $T^{d}$ with non-algebraic nonlinearity

Sharp mass-threshold for Dancer-type solutions of the focusing mass-critical NLS on $R^{d} \times T$