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1 April 2005 Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system
Camillo De Lellis
Duke Math. J. 127(2): 313-339 (1 April 2005). DOI: 10.1215/S0012-7094-04-12724-1

Abstract

We consider the Cauchy problem for the system ∂tui + divz(g(|u|)ui) = 0, i ∈ {1,…, k}, in m space dimensions and with gC3. When k ≥ 2 and m = 2, we show a wide choice of g's for which the bounded variation (BV) norm of admissible solutions can blow up, even when the initial data have arbitrarily small oscillation and arbitrarily small total variation, and are bounded away from the origin. When m ≥ 3, we show that this occurs whenever g is not constant, that is, unless the system reduces to k decoupled transport equations with constant coefficients.

Citation

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Camillo De Lellis. "Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system." Duke Math. J. 127 (2) 313 - 339, 1 April 2005. https://doi.org/10.1215/S0012-7094-04-12724-1

Information

Published: 1 April 2005
First available in Project Euclid: 23 March 2005

zbMATH: 1074.35073
MathSciNet: MR2130415
Digital Object Identifier: 10.1215/S0012-7094-04-12724-1

Subjects:
Primary: 35L65
Secondary: 35L40, 35L45

Rights: Copyright © 2005 Duke University Press

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Vol.127 • No. 2 • 1 April 2005
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