6 citations · 8 across the 7 of their papers we have counts for
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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…
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…
Dissipative solutions for 2D Onsager's conjecture
Lili Du, Xinliang Li, Weikui Ye
In 1949, L. Onsager conjectured that weak solutions of the Euler equations in are energy conservative when , whereas nonconservative solutions exist when…
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 , we resolve the flexible part of Onsager-type conjecture for Elsässer ener…
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…
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 . To be more precise, we exhibit the…
On Onsager's type conjecture for the inviscid Boussinesq equations
Changxing Miao, Yao Nie, Weikui Ye
In this paper, we investigate the Cauchy problem for the three dimensional inviscid Boussinesq system in the periodic setting. For , we show that the threshold re…
Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces
Qionglei Chen, Yao Nie, Weikui Ye
In this paper, we prove a sharp ill-posedness result for the incompressible non-resistive MHD equations. In any dimension , we show the ill-posedness of the non-resistive M…