Siwei Luo Admin

Research

An index of publications, academic talks, and research experience.

Research interests
  • Applied Analysis
  • Partial Differential Equations (PDEs)
  • Kinetic Theory
  • AI4Math
  • Probability Theory

Publications and preprints

2
2026 Preprint
Four panels comparing bulk-controlled, surface-controlled, fractal-interface, and capacity-limited mass exchange.

No Gelation and Global Existence for a Boltzmann Equation with Regularly Varying Mass-Exchange Rates

Siwei Luo and Jian-Guo Liu

Submitted 27 July 2026arXiv:2607.25112 [math.AP]

A tail-adapted no-gelation mechanism that absorbs large–large moment production through a bounded-mass particle reservoir, with the decisive factor $L^{\gamma-1}$, yielding global solutions from the physical moments alone.

2026 Preprint
Horizontal concept diagram of two incoming particles undergoing a two-to-two collision and leaving with redistributed masses.

On the Spatially Homogeneous Boltzmann Equation with Mass Exchange

Siwei Luo and Jian-Guo Liu

Submitted 22 July 2026arXiv:2607.20684 [math.AP]

Global and local Cauchy theories for the spatially homogeneous Boltzmann equation with continuous mass exchange, based on a new two-stage bootstrap without detailed-balance or entropy structures.

Academic talks

2

  1. On the Discrete-to-Continuous Mass Limit for BME

    University of Science and Technology of China · Hefei, Anhui, China

    • Introduces Degond-Liu research on Boltzmann equation with binary mass exchange.
    • Presents discrete-mass to continuous-mass limit result completed by Luo.

  2. On the Discrete-to-Continuous Mass Limit for BME

    Wuhan University · Wuhan, Hubei, China

Academic experience

6

Undergraduate Thesis Research in AI4Math

University of Science and Technology of China · Hefei, Anhui, China

  • Designing an automated qmd-prover agent skill that turns QMD code into rigorous mathematical manuscripts.
Advisor
Prof. Xiao Ma 马骁

Condensation and Gelation

Duke University · Durham, North Carolina, USA

  • Developing adaptations of methods from two papers on the Boltzmann equation with mass exchange, together with new mechanisms, to study condensation and gelation in Bose–Boltzmann equations and wave-turbulence models.
Mentor
Prof. Jian-Guo Liu 刘建国

Boltzmann Equation with Mass Exchange

Duke University · Durham, North Carolina, USA

  • Established global and local Cauchy theories for the spatially homogeneous Boltzmann equation with continuous mass exchange.
  • Developed a no-gelation mechanism for regularly varying mass-exchange rates; the project produced two preprints.
Preprints
On the Spatially Homogeneous Boltzmann Equation with Mass ExchangeNo Gelation and Global Existence for a Boltzmann Equation with Regularly Varying Mass-Exchange Rates
Mentor
Prof. Jian-Guo Liu 刘建国

Discrete-to-Continuous Mass Limit for Binary Mass Exchange

University of Science and Technology of China · Hefei, Anhui, China

  • Studied the discrete-to-continuous mass limit for a spatially homogeneous Boltzmann model with binary mass exchange.
  • Established the limit through uniform a priori estimates, weak time compactness, and identification of the nonlinear collision term.
Mentor
Prof. Shunlin Shen 沈舜麟

Summer Research in Kinetic Theory

Institute of Mathematical Science, Chinese University of Hong Kong · Hong Kong, China

  • Conducted summer research in kinetic theory as an Honorable Research Assistant (junior).
  • Studied Villani’s Fisher-information framework and adapted its Fisher–entropy argument to a finite-velocity discrete kinetic model.
Mentors
Prof. Renjun Duan 段仁军Prof. Zhouping Xin 辛周平

Algebra and Number Theory Summer School

Academy of Mathematics and Systems Science, Chinese Academy of Sciences · Beijing, China

  • Completed intensive courses in algebraic geometry, algebraic number theory, and representation theory of finite groups.
  • Participated in the summer school founded by Prof. Shouwu Zhang 张寿武 of Princeton University.
Program faculty
Prof. Shouwu Zhang 张寿武