Non-uniqueness of weak solutions to 2D generalized Navier-Stokes equations

2024/05/31 by Xinliang Li, Li, Xinliang, Zhong Tan +1 · 1 citation
Computer Science · Engineering · Mathematics · #35A02 #35Q30 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2405.20754

openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces L_t^γL_x^p when α∈[1,(3)/(2)), and obtain the conclusion that the non-uniqueness of the weak solutions at the endpoint (γ,p)=(∞, (2)/(2α-1)) is sharp in view of the generalized Ladyženskaja-Prodi-Serrin condition by using a different spatial-temporal building block from [Cheskidov-Luo, Ann. PDE, 9:13 (2023)] and taking advantage of the intermittency of the temporal concentrated function g_(k) in an almost optimal way. Our results recover the above 2D non-uniqueness conclusion and extend to the hyper-dissipative case α∈(1,(3)/(2)).

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