Recently, the internationally renowned academic journal “Journal de Mathématiques Pures et Appliquées” published a research paper titled “Non-uniqueness of weak solutions to the Navier-Stokes equations in R³” by Assistant Professor Weikui Ye and his collaborators (Professor Changxing Miao from the Institute of Applied Physics and Computational Mathematics in Beijing and Associate Professor Yao Nie from Nankai University) from the Differential Equations and Applications Research Group at the School of Mathematical Sciences, Shenzhen University. This paper investigates the non-uniqueness of weak solutions to the three-dimensional incompressible Navier-Stokes equations in the L² energy framework over the entire space R³. As is well known, the non-uniqueness of weak solutions to the three-dimensional incompressible Navier-Stokes equations on periodic domains was first proven by mathematicians Buckmaster and Vicol in “Annals of Mathematics,” one of the four major mathematics journals. Compared to periodic domains, the core difficulty in the entire space lies in the absence of compactness. This work overcomes the previous reliance on discrete Fourier schemes and spatial compactness in constructions for periodic domains, and for the first time implements a convex integration method for the Navier-Stokes equations under relaxed conditions requiring finite total kinetic energy in unbounded domains. “Journal de Mathématiques Pures et Appliquées” was founded in 1836 by the renowned French mathematician Joseph Liouville. It is a long-standing international mathematics journal that is still in publication today. It primarily publishes groundbreaking and significant results across various fields of pure mathematics and enjoys a high academic reputation.

Full text link:

https://doi.org/10.1016/j.matpur.2026.103920

Biography:

Weikui Ye is an Assistant Professor at the School of Mathematical Sciences, Shenzhen University. He received his Ph.D. in Science from Sun Yat-sen University in 2021 and served as a postdoctoral researcher at the Institute of Applied Physics and Computational Mathematics in Beijing from 2021 to 2023. His research focuses on nonlinear partial differential equations, specifically the Onsager conjecture and related problems of weak solution non-uniqueness. His research findings have been published in internationally renowned journals such as Ann.PDE, JMPA, JFA, JDE, and JNS.