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math.AP2026
Sharp non-uniqueness of weak solutions to 2D magnetohydrodynamic equations
Changxing Miao, Yao Nie, Weikui Ye
In this paper, we prove that weak solutions to the 2D viscous and resistive magnetohydrodynamic (MHD) equations are non-unique in $L^2_t L^p(\mathbb{R}^2) \cap L^1_t W^{1,p}(\mathb…
math.AP2026
Non-uniqueness of smooth solutions to the Navier-Stokes equations on torus $\TTT^2$
Changxing Miao, Yao Nie, Weikui Ye
The local well-posedness theory for the incompressible Navier-Stokes equations in $\BMO^{-1}$ has attracted considerable attention over the past two decades. In a recent breakthrou…