Mimi Dai

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math.AP2026

Instantaneous blowup of incompressible flow with passive tracer

Mimi Dai, Xiaotong "Dawson" Yang

We construct a family of solutions $(u, b)$ of the incompressible flow with a passive tracer for which both $∥ u (t) ∥_{L^{\infty}}$ and $∥ b (t) ∥_{L^{\infty}}$ blow up at time $T_{*}$ . Aw…

math.AP2026

Instantaneous blowup and non-uniqueness of smooth solutions of MHD

Mimi Dai

We construct a family of solutions $(u, B)$ of the incompressible magnetohydrodynamic (MHD) system, the $L^{\infty}$ norm of which blows up instantaneously at the critical rate. The s…

math.AP2026

Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence

Hassan Babaei, Mimi Dai

In turbulent flows, the Kolmogorov wavenumber characterizes the smallest scales at which viscous effects dominate. A mathematical analogue of this notion first introduced by Foias…

math.AP2026

Ill-posedness of $2 \frac{1}{2}$ D electron MHD

Mimi Dai

We consider the electron magnetohydrodynamics (MHD) in the context where the 3D magnetic field depends only on the two horizontal plane variables. In particular, the magnetic field…

Instantaneous blowup of incompressible flow with passive tracer

Instantaneous blowup and non-uniqueness of smooth solutions of MHD

Determining wavenumbers for Hall and electron magnetohydrodynamics turbulence

Ill-posedness of 221​D electron MHD

Ill-posedness of $2 \frac{1}{2}$ D electron MHD