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Publications [#354611] of Xiaoyutao Luo

Papers Published

  1. Cheskidov, A; Luo, X, Nonuniqueness of Weak Solutions for the Transport Equation at Critical Space Regularity, Annals of Pde, vol. 7 no. 1 (June, 2021), Springer Science and Business Media LLC [doi]
    (last updated on 2022/12/04)

    Abstract:
    We consider the linear transport equations driven by an incompressible flow in dimensions d≥ 3. For divergence-free vector fields u∈Lt1W1,q, the celebrated DiPerna-Lions theory of the renormalized solutions established the uniqueness of the weak solution in the class Lt∞Lp when 1p+1q≤1. For such vector fields, we show that in the regime 1p+1q>1, weak solutions are not unique in the class Lt1Lp. One crucial ingredient in the proof is the use of both temporal intermittency and oscillation in the convex integration scheme.

 

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