Non Uniqueness of Power-Law Flows

We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension [Formula: see text] . For the power index q below the compactness threshold, i.e. [Formula: see text] , we show ill-posedness of Leray–Hopf solutions. For a wider class of i...

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Autores principales: Burczak, Jan, Modena, Stefano, Székelyhidi, László
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550025/
https://www.ncbi.nlm.nih.gov/pubmed/34720129
http://dx.doi.org/10.1007/s00220-021-04231-7
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author Burczak, Jan
Modena, Stefano
Székelyhidi, László
author_facet Burczak, Jan
Modena, Stefano
Székelyhidi, László
author_sort Burczak, Jan
collection PubMed
description We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension [Formula: see text] . For the power index q below the compactness threshold, i.e. [Formula: see text] , we show ill-posedness of Leray–Hopf solutions. For a wider class of indices [Formula: see text] 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 [Formula: see text] .
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spelling pubmed-85500252021-10-29 Non Uniqueness of Power-Law Flows Burczak, Jan Modena, Stefano Székelyhidi, László Commun Math Phys Article We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension [Formula: see text] . For the power index q below the compactness threshold, i.e. [Formula: see text] , we show ill-posedness of Leray–Hopf solutions. For a wider class of indices [Formula: see text] 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 [Formula: see text] . Springer Berlin Heidelberg 2021-10-06 2021 /pmc/articles/PMC8550025/ /pubmed/34720129 http://dx.doi.org/10.1007/s00220-021-04231-7 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Burczak, Jan
Modena, Stefano
Székelyhidi, László
Non Uniqueness of Power-Law Flows
title Non Uniqueness of Power-Law Flows
title_full Non Uniqueness of Power-Law Flows
title_fullStr Non Uniqueness of Power-Law Flows
title_full_unstemmed Non Uniqueness of Power-Law Flows
title_short Non Uniqueness of Power-Law Flows
title_sort non uniqueness of power-law flows
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550025/
https://www.ncbi.nlm.nih.gov/pubmed/34720129
http://dx.doi.org/10.1007/s00220-021-04231-7
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