Uniqueness and Nonuniquess for Nonsmooth Divergence Free Transport
Ferruccio Colombini, Tao Luo and Jeffrey Rauch
We present an example of a uniformly bounded divergence free vector field
a(x).∂x on Rd which has the property that the
linear transport equation
has a nontrivial bounded solution with vanishing Cauchy data. The coefficients
have the property that x3∇a is a bounded measure.
∂t u + ∑di=1
aj(t,x) ∂xj u = 0,
div a = ∑di=1 ∂xj
aj = 0 (1)
For the same equation we prove uniqueness in the Cauchy problem when
the coefficients a and u belong to
- Available as PDF (176 Kbytes).
- Ferruccio Colombini,
- Tao Luo,
- Jeffrey Rauch,
- Publishing information:
- Submitted by:
April 21 2004.
Preprint Server Homepage
© The copyright for the following
documents lies with the authors. Copies of these documents made by electronic
or mechanical means including information storage and retrieval systems, may
only be employed for personal use.
Conservation Laws Preprint Server <firstname.lastname@example.org>
Last modified: Thu Apr 22 09:55:06 MEST 2004