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On Uniqueness and Helicity Conservation of Weak Solutions to the Electron-MHD System

https://doi.org/10.1007/s00021-022-00701-7

Dai, Mimi ; Krol, Jacob ; Liu, Han ( August 2022 , Journal of Mathematical Fluid Mechanics)

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Dyadic models for ideal MHD

https://doi.org/10.1007/s00021-021-00640-9

Dai, Mimi ; Friedlander, Susan ( February 2022 , Journal of Mathematical Fluid Mechanics)

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Blow-up of a dyadic model with intermittency dependence for the Hall MHD

https://doi.org/10.1016/j.physd.2021.133066

Dai, Mimi ( December 2021 , Physica D: Nonlinear Phenomena)

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Local well-posedness for the Hall-MHD system in optimal Sobolev spaces

Dai, Mimi ( July 2021 , Journal of differential equations)
null (Ed.)
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Local well-posedness for the Hall-MHD system in optimal Sobolev spaces

Dai, Mimi ( April 2021 , Journal of differential equations)
null (Ed.)
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Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System

Dai, Mimi ( January 2021 , SIAM Journal on Mathematical Analysis)

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Phenomenologies of intermittent Hall MHD turbulence

https://doi.org/10.3934/dcdsb.2021285

Dai, Mimi ( January 2021 , Discrete & Continuous Dynamical Systems - B)

We introduce the concept of intermittency dimension for the magnetohydrodynamics (MHD) to quantify the intermittency effect. With dependence on the intermittency dimension, we derive phenomenological laws for intermittent MHD turbulence with and without the Hall effect. In particular, scaling laws of dissipation wavenumber, energy spectra and structure functions are predicted. Moreover, we are able to provide estimates for energy spectra and structure functions which are consistent with the predicted scalings.

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Application of harmonic analysis techniques to regularity problems of dissipative equations

https://doi.org/10.1090/conm/748/15055

Dai, Mimi ; Liu, Han ( April 2020 , Contemporary mathematics)

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Low modes regularity criterion for a chemotaxis-Navier-Stokes system

https://doi.org/10.3934/cpaa.2020118

Dai, Mimi ; Liu, Han ( January 2020 , Communications on Pure & Applied Analysis)

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Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces

https://doi.org/10.1016/j.jmaa.2019.123493

Cheskidov, Alexey ; Dai, Mimi ( January 2020 , Journal of Mathematical Analysis and Applications)

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