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June 2004 Nearly Lipschitzean Divergence Free Transport Propogates neither Continuity nor BV Regularity
Ferruccio Colombini, Tao Luo, Jeffrey Rauch
Commun. Math. Sci. 2(2): 207-212 (June 2004).

Abstract

We give examples of divergence free vector fields. For such fields the Cauchy problem for the linear transport equation has unique bounded solutions. The first example has nonuniqueness in the Cauchy problem for the ordinary differential equation defining characteristics. In addition, there are smooth initial data so that the unique bounded solution is not continuous on any neighborhood of the origin. The second example is a field of similar regularity and intial data of bounded variation.

Citation

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Ferruccio Colombini. Tao Luo. Jeffrey Rauch. "Nearly Lipschitzean Divergence Free Transport Propogates neither Continuity nor BV Regularity." Commun. Math. Sci. 2 (2) 207 - 212, June 2004.

Information

Published: June 2004
First available in Project Euclid: 1 March 2005

zbMATH: 1088.35015
MathSciNet: MR2119938

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 2 • June 2004
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