Math @ Duke

Publications [#365618] of Xiaoyutao Luo
Papers Published
 Cheskidov, A; Luo, X, Sharp nonuniqueness for the Navier–Stokes equations,
Inventiones Mathematicae, vol. 229 no. 3
(September, 2022),
pp. 9871054 [doi]
(last updated on 2022/12/04)
Abstract: In this paper, we prove a sharp nonuniqueness result for the incompressible Navier–Stokes equations in the periodic setting. In any dimension d≥ 2 and given any p< 2 , we show the nonuniqueness of weak solutions in the class LtpL∞, which is sharp in view of the classical Ladyzhenskaya–Prodi–Serrin criteria. The proof is based on the construction of a class of nonLeray–Hopf weak solutions. More specifically, for any p< 2 , q< ∞, and ε> 0 , we construct nonLeray–Hopf weak solutions u∈LtpL∞∩Lt1W1,q that are smooth outside a set of singular times with Hausdorff dimension less than ε. As a byproduct, examples of anomalous dissipation in the class Lt3/2εC1/3 are given in both the viscous and inviscid case.


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