Nonuniqueness of weak solutions for the transport equation at critical space regularity
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Publication:2040254
DOI10.1007/s40818-020-00091-xzbMath1469.35001arXiv2004.09538OpenAlexW3121115800MaRDI QIDQ2040254
Xiaoyutao Luo, Alexey Cheskidov
Publication date: 12 July 2021
Published in: Annals of PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.09538
Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for systems of linear first-order PDEs (35F46) Transport equations (35Q49)
Related Items (16)
Rigorous results on conserved and dissipated quantities in ideal MHD turbulence ⋮ Sharp nonuniqueness for the Navier-Stokes equations ⋮ Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations ⋮ The nontrivial weak solution of Boussinesq system in high dimensions ⋮ Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients ⋮ \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations ⋮ Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields ⋮ On the failure of the chain rule for the divergence of Sobolev vector fields ⋮ Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence ⋮ A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity ⋮ Non-conservative solutions of the Euler-\(\alpha\) equations ⋮ Weak and parabolic solutions of advection-diffusion equations with rough velocity field ⋮ Non uniqueness of power-law flows ⋮ A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation ⋮ On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations
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