6 papers
A multidimensional Szemerédi theorem in integers
Jingwei Guo, Changxing Miao, Guoqing Zhan
For any integer , let be a strictly increasing -tuple of positive integers. We show that any subset of density at least $(\log…
Improvement of Pólya's conjecture for balls and cylinders
Jingwei Guo, Changxing Miao, Weiwei Wang +1
Pólya's conjecture on the eigenvalues of the Laplacian has been one of the core problems in spectral geometry. Building upon the recent breakthrough works on Pólya's conjecture f…
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 ene…
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…
Two-point polynomial patterns in subsets of positive density in
Xuezhi Chen, Changxing Miao
Let where is a real polynomial with zero constant term for each . We will show the existence of the configuration $\{x,x+γ(t)\}…