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math.AP2026
Non-uniqueness for the hyperdissipative Navier-Stokes equations with arbitrarily small subcritical data
Zipeng Chen, Song Liu, Zhaoyang Yin
In this paper, we consider the hyperdissipative Navier-Stokes equations with fractional dissipation with . We prove that smooth solutions of the hyperdissipative Navi…
math.AP2026
Finite-time blow-up for the Geng--Xue system with an application to the three-component Degasperis--Procesi system
Song Liu, Zhaoyang Yin
We prove finite-time blow-up for the Geng--Xue system with initial data satisfying and at Sobolev regularity , where .…
math.AP2026
Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data
Zipeng Chen, Song Liu, Zhaoyang Yin
Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in . Insp…