Changxing Miao

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math.AP2025

On Onsager-type conjecture for the Elsässer energies of the ideal MHD equations

Changxing Miao, Yao Nie, Weikui Ye

In this paper, we investigate the ideal magnetohydrodynamics (MHD) equations on tours $\TTT^d$. For $d = 3$ , we resolve the flexible part of Onsager-type conjecture for Elsässer ener…

math.AP2024

Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3

Changxing Miao, Yao Nie, Weikui Ye

To our knowledge, the convex integration method has been widely applied to the study of non-uniqueness of solutions to the Naiver-Stokes equations in the periodic region, but there…

math.AP2024

Sharp non-uniqueness for the Navier-Stokes equations in R^3

Changxing Miao, Yao Nie, Weikui Ye

In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the incompressible Navier-Stokes equations in $R^{3}$ . To be more precise, we exhibit the…

math.AP2024

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$

Changxing Miao, Lixin Yan, Junyong Zhang

We study $L^{p}$ -boundedness of the Bochner-Riesz means for critical magnetic Schrödinger operators $L_{A}$ in $R^{2}$ , which involve the physcial Aharonov-Boh…

On Onsager-type conjecture for the Elsässer energies of the ideal MHD equations

Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3

Sharp non-uniqueness for the Navier-Stokes equations in R^3

Bochner-Riesz means for critical magnetic Schrödinger operators in R2

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$