Work

Sharp non‐uniqueness for the 2D hyper‐dissipative Navier–Stokes equations

Year: 2025

Type: article

Abstract: In this paper, we study the non‐uniqueness of weak solutions for the two‐dimensional hyper‐dissipative Navier–Stokes equations (NSE) in the super‐critical spaces when the viscosity exponent , and obtain the conclusion that the non‐uniqueness of the weak solutions at the two endpoints is sharp in view of the generalized Ladyženskaya–Prodi–Serrin condition with the triplet and . By using the intermittency of the temporal concentrated function in an almost optimal way, we extend the recent elegant works on the non‐uniqueness of 2D NSE in Cheskidov and Luo [Invent. Math. 229 (2022), no. 3, 987–1054] and [Ann. PDE, 9 (2023), no. 2, Paper No. 13] to the hyper‐dissipative case . In particularly, the viscosity exponent is the upper limit for the one endpoint case when .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70317

Authors: Lili Du, Xinliang Li

Institutions: Shenzhen University, Sichuan University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation

Awards: G2168035697, G2936774632, G4747111955, G6387906360