60 citations · 272 across the 21 of their papers we have counts for
22 papers
The four-dimensional Anderson model: a case study for critical SPDEs
Yu Deng, Hao Shen
We study the weakly coupled elliptic Anderson model with spatial white noise on the four-dimensional torus, which provides a basic example of a critical SPDE requiring renormalizat…
On the wave turbulence theory of 2D gravity waves, I: deterministic energy estimates
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received…
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…
Propagation of chaos and the higher order statistics in the wave kinetic theory
Yu Deng, Zaher Hani
This manuscript continues and extends in various directions the result in arXiv:2104.11204, which gave a full derivation of the wave kinetic equation (WKE) from the nonlinear Schrö…
Full derivation of the wave kinetic equation
Yu Deng, Zaher Hani
We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that de…
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 Smallness Condition in Linear Inviscid Damping: Monotonicity and Resonance Chains
Yu Deng, Christian Zillinger
We consider the linearized Euler equations around a smooth, bilipschitz shear profile on . We construct an explicit flow which exhibits linea…
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics
Yu Deng, Christian Zillinger
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to…
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…
Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori
Yu Deng, Pierre Germain, Larry Guth +1
We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one…
On the global behavior of weak null quasilinear wave equations
Yu Deng, Fabio Pusateri
We consider a class of quasilinear wave equations in space-time dimensions that satisfy the "weak null condition" as defined by Lindblad and Rodnianski \cite{LR1}, and study…
Long time instability of the Couette flow in low Gevrey spaces
Yu Deng, Nader Masmoudi
We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem s…
Strichartz estimates for the Schrodinger equation on irrational tori
Yu Deng, Pierre Germain, Larry Guth
We prove Strichartz estimates over large time scales for the Schrodinger equation set on irrational tori. They are optimal for Lebesgue exponents .
Growth of higher Sobolev norms for energy critical NLS on irrational tori: small energy case
Yu Deng
We consider the energy critical nonlinear Schrodinger equation on generic irrational tori. Using the long-time Strichartz estimates proved in [8], we establish polynomial upper bou…
Growth of solutions to NLS on irrational tori
Yu Deng, Pierre Germain
We prove polynomial bounds on the growth of higher Sobolev norms for the nonlinear Schrodinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearit…
The Euler--Maxwell system for electrons: global solutions in
Yu Deng, Alexandru D. Ionescu, Benoit Pausader
A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagn…
Multispeed Klein-Gordon systems in dimension three
Yu Deng
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a lin…
Global solutions of the gravity-capillary water-wave system in three dimensions
Y. Deng, A. D. Ionescu, B. Pausader +1
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem prese…
Invariant measures and long time behaviour for the Benjamin-Ono equation III
Y. Deng, N. Tzvetkov, N. Visciglia
We complete the program developed in our previous works aiming to construct an infinite sequence of invariant measures of gaussian type associated with the conservation laws of the…
Invariance of the Gibbs measure for the Benjamin-Ono equation
Yu Deng
In this paper we consider the periodic Benjemin-Ono equation. We will establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in…
Two Dimensional NLS Equation With Random Radial Data
Yu Deng
In this paper we study radial solutions of certain two-dimensional nonlinear Schrödinger equation with harmonic potential, which is supercritical with respect to the initial data.…