Exponential self-similar mixing and loss of regularity for continuity equations

Alberti, Giovanni and Crippa, Gianluca and Mazzucato, Anna L.. (2014) Exponential self-similar mixing and loss of regularity for continuity equations. Comptes rendus mathematique, Vol. 352, no. 11. pp. 901-906.

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Official URL: http://edoc.unibas.ch/dok/A6329037

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We consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity eld. In this announcement we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity elds, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity eld exhibiting instantaneous loss of any fractional Sobolev regularity.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Académie de Sciences
Note:Publication type according to Uni Basel Research Database: Journal article
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edoc DOI:
Last Modified:31 Dec 2015 10:56
Deposited On:09 Jan 2015 09:25

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