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math.AP2026
Low-regularity invariant measure for the complex-valued mKdV
Zachary Lee, NataÅ¡a PavloviÄ, Gigliola Staffilani +1
In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an…
math.AP2024
Global well-posedness and scattering for the defocusing septic one-dimensional NLS via new smoothing and almost Morawetz estimates
Zachary Lee, Xueying Yu
In this paper, we show that the one dimensional septic nonlinear Schrödinger equation is globally well-posed and scatters in when . We prove new smoo…
math.AP2024
On uniqueness properties of solutions of the generalized fourth-order Schrödinger equations
Zachary Lee, Xueying Yu
In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension of the following forms, $$i \partial_t u + \s…