Yongming Luo

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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…

math.AP2025

Critical scattering for the nonlinear SchrÃ¶dinger equation on waveguide manifolds

Yongming Luo

We study the small data scattering problem in critical spaces for the nonlinear SchrÃ¶dinger equation (NLS) on waveguide manifolds. Our work is primarily inspired by the recent pap…

math.AP2024

Solitons, scattering and blow-up for the nonlinear SchrÃ¶dinger equation with combined power-type nonlinearities on $R^{d} \times T$

Luigi Forcella, Yongming Luo, Zehua Zhao

We investigate the long time dynamics of the nonlinear SchrÃ¶dinger equation (NLS) with combined powers on the waveguide manifold $R^{d} \times T$ . Different from the…

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

Critical scattering for the nonlinear SchrÃ¶dinger equation on waveguide manifolds

Solitons, scattering and blow-up for the nonlinear SchrÃ¶dinger equation with combined power-type nonlinearities on Rd×T

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 $R^{d} \times T$

Solitons, scattering and blow-up for the nonlinear SchrÃ¶dinger equation with combined power-type nonlinearities on $R^{d} \times T$