Calculus of Variations and Geometric Measure Theory
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S. Modena - L. J. Székelyhidi

Non-uniqueness for the transport equation with Sobolev vector fields

created by modena on 12 Dec 2017
modified on 28 Dec 2017

[BibTeX]

Preprint

Inserted: 12 dec 2017
Last Updated: 28 dec 2017

Pages: 30
Year: 2017

ArXiv: 1712.03867v2 [math.AP] PDF

Abstract:

We construct a large class of examples of non-uniqueness for the linear transport equation and the transport-diffusion equation with divergence-free vector fields in Sobolev spaces $W^{1,p}$.

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