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

We study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces Lₓ^Lₗ^p when 1, 32), and obtain the conclusion that the non-uniqueness of the weak solutions at the endpoint (, p) = (, 22-1) is sharp in view of the generalized Ladyzenskaja-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 (₊) in an almost optimal way. Our results recover the above 2D non-uniqueness conclusion and extend to the hyper-dissipative case (1, 32).