Yu Deng邓煜
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Research & publications研究与论文

Research & publications

研究与论文

My current research themes, projects, public resources, and complete publication record.

当前研究方向、科研项目、公开资源与完整论文记录。

I study how macroscopic and statistical laws emerge from microscopic particle and wave dynamics. My work combines partial differential equations with probability and combinatorial expansions, with recent emphasis on the Boltzmann equation, wave kinetic equations, and nonlinear dispersive models.

我研究宏观与统计规律如何从微观粒子和波动力学中产生。工作结合偏微分方程、概率与组合展开，近期重点包括玻尔兹曼方程、波动动理学方程和非线性色散模型。

Read the IMU research citation阅读 IMU 研究评述
01

Kinetic theory and wave turbulence动力学理论与波湍流

How do effective kinetic equations emerge from microscopic particle and wave dynamics, and for how long do they remain valid?有效的动力学方程如何从微观粒子和波动力学中产生，又能在多长时间尺度上保持有效？

I study rigorous derivations of the Boltzmann equation and the wave kinetic equation. A recurring problem is to control an enormous collection of interactions long enough for macroscopic statistics to emerge.我研究玻尔兹曼方程与波动动理学方程的严格推导。反复出现的难点，是在足够长的时间里控制数量庞大的相互作用，使宏观统计规律真正显现。

Representative work代表成果
02

Probabilistic PDEs概率偏微分方程

Can randomness reveal global dynamics beyond the range of deterministic well-posedness?随机性是否能揭示确定性适定性范围之外的整体动力学？

I use invariant Gibbs measures, random tensors, and propagation of randomness to study nonlinear dispersive equations. The goal is not merely to randomize data, but to identify structures that persist through nonlinear evolution.我用不变 Gibbs 测度、随机张量与随机性传播研究非线性色散方程。目标不只是把初值随机化，而是识别在非线性演化中仍能保留下来的结构。

Representative work代表成果

Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two

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03

Statistical physics and quantum field theory统计物理与量子场论

Which probabilistic structures from statistical mechanics survive in infinite-dimensional nonlinear evolution?统计力学中的哪些概率结构能够在无限维非线性演化中保持稳定？

My interests here center on Gibbs measures, equilibrium ensembles, and nonlinear wave models that connect dispersive PDEs with statistical mechanics and quantum field theory.这里的兴趣集中在 Gibbs 测度、平衡系综，以及把色散偏微分方程与统计力学、量子场论联系起来的非线性波模型。

Representative work代表成果

Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three

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04

Inviscid and Landau damping无黏与朗道阻尼

How do mixing, resonance, and echo chains govern stability or instability in fluid and kinetic equations?混合、共振与回波链如何决定流体和动力学方程的稳定或不稳定？

I study long-time mechanisms in Couette flow and related equations, where apparently small resonances can accumulate into instability and where mixing can still produce effective damping.我研究 Couette 流及相关方程中的长时间机制：看似很小的共振如何累积成不稳定性，以及混合如何仍然产生有效阻尼。

Representative work代表成果
05

Future interests未来兴趣

What other geometric or dynamical structures can be reached with these tools?这些方法还能抵达哪些几何或动力学结构？

Questions I may pursue include random geometry, formation and non-formation of singularities, and infinite-dimensional KAM theory.未来可能探索随机几何、奇点的形成与不形成，以及无限维 KAM 理论。

Projects & support科研项目与支持

  • NSF DMS-2246908 / DMS-2531437Principal investigator项目负责人
  • Simons Collaboration on Wave TurbulenceResearch Scientist研究科学家
  • NSF DMS-1900251Principal investigator项目负责人

Research resources研究资源

Lecture 1Lectures 2–3Lecture 4Lecture 5Boltzmann proof overview玻尔兹曼方程证明导读Toy-model algorithms玩具模型算法Simons Foundation filmSimons Foundation 人物短片

Publication record论文记录

30total works项成果
25published & accepted已发表或接收
3preprints预印本
2expository综述文章
CV updated July 26, 2026CV 更新于 2026 年 7 月 26 日Google Scholar

2026

3 works项成果

  1. Long time derivation of Boltzmann equation from hard sphere dynamics

    Y. Deng, Z. Hani and X. Ma

    Annals of Mathematics, to appear.

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  2. Derivation of the wave kinetic equation: full range of scaling laws

    Y. Deng and Z. Hani

    Memoirs of the American Mathematical Society, to appear.

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  3. Propagation of chaos and the higher order statistics in the wave kinetic theory

    Y. Deng and Z. Hani

    Journal of the European Mathematical Society 28 (2026), no. 2, 673–733.

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2025

3 works项成果

  1. On the wave turbulence theory of 2D gravity waves, I: deterministic energy estimates

    Y. Deng, A. Ionescu and F. Pusateri

    Communications on Pure and Applied Mathematics 78 (2025), no. 2, 211–322.

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  2. On the wave turbulence theory of 2D gravity waves, II: propagation of randomness

    Y. Deng, A. Ionescu and F. Pusateri

    arXiv:2504.14304.

    arXivGoogle Scholar

  3. Hilbert’s sixth problem: derivation of fluid equations via Boltzmann’s kinetic theory

    Y. Deng, Z. Hani and X. Ma

    arXiv:2503.01800.

    arXivGoogle Scholar

2024

3 works项成果

  1. Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two

    Y. Deng, A. Nahmod and H. Yue

    Annals of Mathematics 200 (2024), no. 2, 399–486.

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  2. Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation

    B. Bringmann, Y. Deng, A. Nahmod and H. Yue

    Inventiones Mathematicae 236 (2024), no. 3, 1133–1411.

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  3. The probabilistic scaling paradigm

    Y. Deng, A. Nahmod and H. Yue

    Vietnam Journal of Mathematics 52 (2024), no. 4, 1001–1015.

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2023

3 works项成果

  2. Long time instability of the Couette flow in low Gevrey spaces

    Y. Deng and N. Masmoudi

    Communications on Pure and Applied Mathematics 76 (2023), no. 10, 2804–2887.

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2022

3 works项成果

  1. Random tensors, propagation of randomness, and nonlinear dispersive equations

    Y. Deng, A. Nahmod and H. Yue

    Inventiones Mathematicae 228 (2022), no. 2, 539–686.

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  2. Strichartz estimates for the Schrödinger equation on non-rectangular two-dimensional tori

    Y. Deng, P. Germain, L. Guth and S. Myerson

    American Journal of Mathematics 144 (2022), no. 3, 701–745.

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2021

4 works项成果

  1. On the derivation of the wave kinetic equation for NLS

    Y. Deng and Z. Hani

    Forum of Mathematics, Pi 9 (2021), e6, 1–37.

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  2. Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three

    Y. Deng, A. Nahmod and H. Yue

    Journal of Mathematical Physics 62 (2021), 031514.

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  3. Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation

    Y. Deng, A. Nahmod and H. Yue

    Communications in Mathematical Physics 384 (2021), no. 2, 1061–1107.

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  4. Echo chains as a linear mechanism: norm inflation, modified exponents and asymptotics

    Y. Deng and C. Zillinger

    Archive for Rational Mechanics and Analysis 242 (2021), no. 1, 643–700.

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2020

2 works项成果

  1. On the smallness condition in linear inviscid damping: monotonicity and resonance chains

    Y. Deng and C. Zillinger

    Nonlinearity 33 (2020), no. 11, 6176–6194.

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  2. On the global behavior of weak null quasilinear wave equations

    Y. Deng and F. Pusateri

    Communications on Pure and Applied Mathematics 73 (2020), no. 5, 1035–1099.

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2019

2 works项成果

  1. On growth of Sobolev norms for energy critical NLS on irrational tori: Small energy case

    Y. Deng

    Communications on Pure and Applied Mathematics 72 (2019), no. 4, 801–834.

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  2. Growth of solutions to NLS on irrational tori

    Y. Deng and P. Germain

    International Mathematics Research Notices 2019, no. 9, 2919–2950.

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2018

1 works项成果

  1. Multispeed Klein–Gordon systems in dimension three

    Y. Deng

    International Mathematics Research Notices 2018, no. 19, 6070–6144.

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2017

3 works项成果

  1. Strichartz estimates for the Schrödinger equation on irrational tori

    Y. Deng, P. Germain and L. Guth

    Journal of Functional Analysis 273 (2017), no. 9, 2846–2869.

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  2. Global solutions of the gravity-capillary water wave system in three dimensions

    Y. Deng, A. Ionescu, B. Pausader and F. Pusateri

    Acta Mathematica 219 (2017), no. 2, 213–402.

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  3. The Euler–Maxwell system for electrons: global solutions in 2D

    Y. Deng, A. Ionescu and B. Pausader

    Archive for Rational Mechanics and Analysis 225 (2017), no. 2, 771–871.

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2015

2 works项成果

  1. Invariant measures and long time behaviour for the Benjamin–Ono equation III

    Y. Deng, N. Tzvetkov and N. Visciglia

    Communications in Mathematical Physics 339 (2015), no. 3, 815–857.

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  2. Invariance of the Gibbs measure for the Benjamin–Ono equation

    Y. Deng

    Journal of the European Mathematical Society 17 (2015), no. 5, 1107–1198.

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2012

1 works项成果

  1. Two-dimensional nonlinear Schrödinger equation with random radial data

    Y. Deng

    Analysis & PDE 5 (2012), no. 5, 913–960.

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