Publication: Smoothing does not give a selection principle for transport equations with bounded autonomous fields
Smoothing does not give a selection principle for transport equations with bounded autonomous fields
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De Lellis, C., & Giri, V. (2022). Smoothing does not give a selection principle for transport equations with bounded autonomous fields. Annales Mathématiques Du Québec, 46(1), 27–39. https://doi.org/10.1007/s40316-021-00160-y
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We give an example of a bounded divergence free autonomous vector field in R3 (and of a nonautonomous bounded divergence free vector field in R2) and of a smooth initial data for which the Cauchy problem for the corresponding transport equation has 2 distinct solutions. We then show that both solutions are limits of classical solutions of transport equations for appropriate smoothings of the vector fields and of the initial data.
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- De Lellis, Camillo
- Giri, Vikram
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De Lellis, C., & Giri, V. (2022). Smoothing does not give a selection principle for transport equations with bounded autonomous fields. Annales Mathématiques Du Québec, 46(1), 27–39. https://doi.org/10.1007/s40316-021-00160-y
