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Non Uniqueness of Power-Law Flows

Burczak, Jan ; Modena, Stefano ; Székelyhidi, László (2024)
Non Uniqueness of Power-Law Flows.
In: Communications in Mathematical Physics, 2021, 388 (1)
doi: 10.26083/tuprints-00023437
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Item Type: Article
Type of entry: Secondary publication
Title: Non Uniqueness of Power-Law Flows
Language: English
Date: 18 March 2024
Place of Publication: Darmstadt
Year of primary publication: November 2021
Place of primary publication: Berlin ; Heidelberg
Publisher: Springer
Journal or Publication Title: Communications in Mathematical Physics
Volume of the journal: 388
Issue Number: 1
DOI: 10.26083/tuprints-00023437
Corresponding Links:
Origin: Secondary publication DeepGreen
Abstract:

We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension d >= 3. For the power index q below the compactness threshold, i.e. q ∈ (1, 2d/d+2), we show ill-posedness of Leray–Hopf solutions. For a wider class of indices q ∈ (1, 3d+2/d+2) we show ill-posedness of distributional (non-Leray–Hopf) solutions, extending the seminal paper of Buckmaster & Vicol [10]. In this wider class we also construct non-unique solutions for every datum in L²

Uncontrolled Keywords: Theoretical, Mathematical and Computational Physics, Mathematical Physics, Quantum Physics, Complex Systems, Classical and Quantum Gravitation, Relativity Theory
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234378
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Analysis
Date Deposited: 18 Mar 2024 13:38
Last Modified: 30 Apr 2024 09:34
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23437
PPN: 23437
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