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
Article, Secondary publication, Publisher's Version
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Item Type: | Article |
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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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