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Creators/Authors contains: "Ouyang, Zhimeng"

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  1. ; (, Communications in Mathematical Physics)
    Free, publicly-accessible full text available December 1, 2025
  2. ; ; ; (, Discrete and Continuous Dynamical Systems)
    Free, publicly-accessible full text available January 1, 2026
  3. ; ; ; (, SIAM Journal on Mathematical Analysis)
    Full Text Available 
  4. ; (, Archive for Rational Mechanics and Analysis)
    We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equa- tion in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy and entropy densities are bounded above, and the mass density is bounded away from a vacuum, we obtain an estimate of the L∞ norm of the solution de- pending on the macroscopic bounds on these hydrodynamic quantities only. This is a regularization effect in the sense that the initial data is not required to be bounded. We present a proof based on variational ideas, which is fundamentally different to the proof that was previously known for the equation in periodic spatial domains 
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  5. ; (, Kinetic and Related Models)
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  6. ; ; (, Quarterly of Applied Mathematics)
    The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau (r-LAN) equation are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the one-species r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations. 
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  7. ; ; ; (, Nonlinearity)
    Abstract We show that solutions to the Ablowitz–Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely L 2 initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations. 
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  8. ; ; (, Archive for Rational Mechanics and Analysis)
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  9. ; (, Journal of Differential Equations)
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  10. ; (, SIAM Journal on Mathematical Analysis)
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