AI Article Synopsis
- The technique of convex integration is used to demonstrate both non-uniqueness and existence results for power-law fluids in specified dimensions.
- For power indices below the compactness threshold, the study reveals that Leray-Hopf solutions are ill-posed.
- It also shows ill-posedness for a broader range of distributional solutions, building on previously established work, and constructs non-unique solutions for all initial conditions in that broader class.
Article Abstract
We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension . For the power index below the compactness threshold, i.e. , we show ill-posedness of Leray-Hopf solutions. For a wider class of indices 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 .
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550025 | PMC |
| http://dx.doi.org/10.1007/s00220-021-04231-7 | DOI Listing |
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