5 papers
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…
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 .…
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…
-Stability for complex Monge-Ampère equations
Songchen Liu, Liyou Zhang
We first establish the weak stability results for solutions of complex Monge-Ampère equations in relative full mass classes, extending the results known to hold in the full mass cl…
Characterizing the range of the complex Monge-Ampère operator
Songchen Liu
In this note, we solve the complex Monge-Ampère equation for measures with a pluripolar part in compact Kähler manifolds. This result generalizes the classical results obtained by…