Burczak, Jan ; Modena, Stefano ; Székelyhidi, László (2021)
Non Uniqueness of Power-Law Flows.
In: Communications in Mathematical Physics, 388 (1)
doi: 10.1007/s00220-021-04231-7
Article, Bibliographie
This is the latest version of this item.
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
| Item Type: | Article |
|---|---|
| Erschienen: | 2021 |
| Creators: | Burczak, Jan ; Modena, Stefano ; Székelyhidi, László |
| Type of entry: | Bibliographie |
| Title: | Non Uniqueness of Power-Law Flows |
| Language: | English |
| Date: | November 2021 |
| Place of Publication: | Berlin ; Heidelberg |
| Publisher: | Springer |
| Journal or Publication Title: | Communications in Mathematical Physics |
| Volume of the journal: | 388 |
| Issue Number: | 1 |
| DOI: | 10.1007/s00220-021-04231-7 |
| Corresponding Links: | |
| 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 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Analysis |
| Date Deposited: | 19 Mar 2024 10:47 |
| Last Modified: | 19 Mar 2024 10:47 |
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| Suche nach Titel in: | TUfind oder in Google |
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Non Uniqueness of Power-Law Flows. (deposited 18 Mar 2024 13:38)
- Non Uniqueness of Power-Law Flows. (deposited 19 Mar 2024 10:47) [Currently Displayed]
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