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Award ID contains: 2308208

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  1. ; ; ; (, Nonlinearity)
    Abstract We study some dyadic models for incompressible magnetohydrodynamics and Navier–Stokes equation. The existence of fixed point and stability of the fixed point are established. The scaling law of Kolmogorov’s dissipation wavenumber arises from heuristic analysis. In addition, a time-dependent determining wavenumber is shown to exist; moreover, the time average of the determining wavenumber is proved to be bounded above by Kolmogorov’s dissipation wavenumber. Additionally, based on the knowledge of the fixed point and stability of the fixed point, numerical simulations are performed to illustrate the energy spectrum in the inertial range below Kolmogorov’s dissipation wavenumber. 
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  2. (, Applied Mathematical Modelling)
    Free, publicly-accessible full text available October 1, 2026
  3. (, Transactions of the American Mathematical Society)
    We propose one-dimensional reduced models for the three-dimensional electron magnetohydrodynamics which involves a highly nonlinear Hall term with intricate structure. The models contain nonlocal nonlinear terms which are more singular than that of the one-dimensional models for the Euler equation and the surface quasi-geostrophic equation. Local well-posedness is obtained in certain circumstances. Moreover, for a model with nonlocal transport term, we show that singularity develops in finite time for a class of initial data. 
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    Free, publicly-accessible full text available June 1, 2026
  4. ; (, Evolution Equations and Control Theory)
    Free, publicly-accessible full text available January 1, 2026
  5. ; (, Physica D: Nonlinear Phenomena)
    Free, publicly-accessible full text available November 1, 2025
  6. (, Journal of Mathematical Fluid Mechanics)
    Full Text Available 
  7. (, Discrete and Continuous Dynamical Systems - B)
    Full Text Available 
  8. ; (, Journal of Differential Equations)
    Full Text Available 
  9. ; ; (, Journal of Nonlinear Science)
    Full Text Available 
  10. ; ; (, Journal of Mathematical Fluid Mechanics)
    Full Text Available