Zipeng Chen

collaborators

4 papers

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 $(- I^)^{2}$ with $I^^{2} > 1$ . We prove that smooth solutions of the hyperdissipative N…

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 $B M O^{- 1}$ . Insp…

math.AP2025

Sharp non-uniqueness for the Boussinesq equation with fractional dissipation

Zipeng Chen, Zhaoyang Yin

This paper focuses on the $d$ -dimensional ( $d \geq 2$ ) Boussinesq equation with fractional dissipation $(- I^)^{I^} \pm$ on the torus. We show that the uniqueness property breaks down withi…

math.AP2025

HÃ¶lder continuous weak solutions of the 3D Boussinesq equation with thermal diffusion

Zipeng Chen, Zhaoyang Yin

In this paper, we show the existence of HÃ¶lder continuous periodic weak solutions of the 3D Boussinesq equation with thermal diffusion, which apprroximate the Onsager's critical s…