27 citations · 129 across the 17 of their papers we have counts for
17 papers
Invariant Gibbs measures and global dynamics for fractional cubic Schrödinger equations on the torus
Yuzhao Wang, Haitian Yue, Chenyuan Zhang +1
We consider the defocusing Wick-ordered cubic fractional nonlinear Schrödinger equation on the two-dimensional torus with dispersion relation . In the weakly dispersive…
Nonlinear Schrödinger equation with Ornstein-Uhlenbeck operator
Xueying Yu, Haitian Yue, Zehua Zhao
In this work, we introduce and study nonlinear Schrödinger equations (NLS) with anisotropic dispersion, where the standard Laplacian acts on the Euclidean variable \(x \in \mathbb{…
The probabilistic scaling paradigm
Yu Deng, Andrea R. Nahmod, Haitian Yue
In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlin…
On well-posedness results for the cubic-quintic NLS on
Yongming Luo, Xueying Yu, Haitian Yue +1
We consider the periodic cubic-quintic nonlinear Schrödinger equation \begin{align}\label{cqnls_abstract} (i\partial_t +Δ)u=μ_1 |u|^2 u+μ_2 |u|^4 u\tag{CQNLS} \end{align} on the th…
Singular Levy processes and dispersive effects of generalized Schrödinger equations
Yannick Sire, Xueying Yu, Haitian Yue +1
We introduce new models for Schrödinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to under…
Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
Bjoern Bringmann, Yu Deng, Andrea R. Nahmod +1
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic -model. This result is th…
On the decay property of the cubic fourth-order Schrödinger equation
Xueying Yu, Haitian Yue, Zehua Zhao
In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on () enjoys the same (pointwise) decay proper…
Global Well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we study the well-posedness theory and the scattering asymptotics for fourth-order Schrödinger equations (4NLS) on waveguide manifolds (semiperiodic spaces) $\mathbb…
Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three
Yu Deng, Andrea R. Nahmod, Haitian Yue
In this paper we consider the defocusing Hartree nonlinear Schrödinger equations on with real valued and even potential and Fourier multiplier decaying like $|k|^…
On the global well-posedness for the periodic quintic nonlinear Schrödinger equation
Xueying Yu, Haitian Yue
In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on with general data in the critical Sobolev space $H^{\f…
Global Well-posedness for the focusing cubic NLS on the product space
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space with initial data bel…
Random tensors, propagation of randomness, and nonlinear dispersive equations
Yu Deng, Andrea R. Nahmod, Haitian Yue
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXi…
Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
Yu Deng, Andrea R. Nahmod, Haitian Yue
We consider the defocusing nonlinear Schrödinger equation on with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the as…
Optimal local well-posedness for the periodic derivative nonlinear Schrodinger equation
Yu Deng, Andrea R. Nahmod, Haitian Yue
We prove local well-posedness for the periodic derivative nonlinear Schrodinger's equation, which is L^2 critical, in Fourier-Lebesgue spaces which scale like H^s(T) for s>0. In pa…
Almost sure well-posedness for the cubic nonlinear Schrödinger equation in the super-critical regime on $\TTT^d$,
Haitian Yue
In this paper we prove almost sure local well-posedness in both atomic spaces and Fourier restriction spaces for the cubic nonlinear Schrödinger equation on $\TTT^…
Global Well-Posedness of the Energy-Critical Nonlinear Schrödinger Equation on
Haitian Yue
In this paper, we first prove global well-posedness for the defocusing cubic nonlinear Schrödinger equation (NLS) on 4-dimensional tori - either rational or irrational - and with i…
Self trapping transition for a nonlinear impurity within a linear chain
Haitian Yue, Mario I. Molina, Panayotis G. Kevrekidis +1
In the present work we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schrödinger chain exampl…