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Formation of singularities for multi-dimensional transport equations with nonlocal velocity

Abstract

This paper is concerned with a class of multi-dimensional transport equations with nonlocal velocity. It is shown that the local smooth solution cannot exist globally in time via the De Giorgi iteration technique.

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Acknowledgements

Q. Jiu was partially supported by the National Natural Science Foundation of China (NNSFC) (No. 11931010, No. 12061003) and a key research project of the Academy for Multidisciplinary Studies of CNU.

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Correspondence to Quansen Jiu.

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Jiu, Q., Zhang, W. Formation of singularities for multi-dimensional transport equations with nonlocal velocity. JAMA 146, 385–400 (2022). https://doi.org/10.1007/s11854-022-0197-4

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  • DOI: https://doi.org/10.1007/s11854-022-0197-4