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math.AP2025
Sharper bounds on the box-counting dimension of singularities in the hyperdissipative Navier-Stokes system
Min Jun Jo
We study upper bounds on the box-counting dimension of the set of potential singular points in suitable weak solutions to the 3D incompressible hyperdissipative Navier-Stokes syste…
math.AP2025
Sharp asymptotic stability of the incompressible porous media equation
Roberta Bianchini, Min Jun Jo, Jaemin Park +1
In this paper, we prove the asymptotic stability of the incompressible porous media (IPM) equation near a stable stratified density, for initial perturbations in the Sobolev space…
math.AP2025
Cusp Formation in Vortex Patches
Tarek M. Elgindi, Min Jun Jo
We prove instantaneous cusp formation for any initial vortex patch with acute corners. This was conjectured to occur in the numerical literature.