Abstract:We consider the Cauchy problem for the system ∂_{t}u_{i}+ ∇_{z}(g(|u|) u_{i}) = 0, i∈{1,…,k}, inmspace dimensions and with g∈C3. When k≥2 and m=2 we show a wide choice ofg's for which the BV norm of admissible solutions can blow up, even when the initial data have arbitrarily small oscillation, arbitrarily small total variation, and are bounded away from the origin. When m≥3 we show that this occurs whenevergis not constant, i.e. unless the system reduces tokdecoupled transport equations with constant coefficients.

**Paper:**- Available as gzipped PostScript (120 Kbytes; uncompress using gunzip).
**Author(s):**- Camillo De Lellis, <delellis@math.unizh.ch>
**Publishing information:**- To appear in Duke Mathematical Journal
**Comments:****Submitted by:**- <delellis@math.unizh.ch> October 12 2004.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | All Preprints | Preprint Server Homepage ]

Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Wed Oct 13 09:40:12 MEST 2004