Smooth approximation is not a selection principle for the transport equation with rough vector field

DOI10.1007/s00526-019-1659-0zbMath1428.35082arXiv1902.08084OpenAlexW3103427171WikidataQ114229051 ScholiaQ114229051MaRDI QIDQ2278132

Gianluca Crippa, Gennaro Ciampa, Stefano Spirito

Publication date: 9 December 2019

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08084

zbMATH Keywords

selection problem for weak solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Navier-Stokes equations (35Q30) Hyperbolic conservation laws (35L65) Initial value problems for nonlinear first-order PDEs (35F25) Initial value problems for linear first-order PDEs (35F10) One-parameter continuous families of measure-preserving transformations (28D10) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence ⋮ Smooth approximation is not a selection principle for the transport equation with rough vector field ⋮ On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity ⋮ Smoothing does not give a selection principle for transport equations with bounded autonomous fields

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