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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Detalles Bibliográficos
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
Descripción
Sumario: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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