@article {2014,
title = {Renormalization for autonomous nearly incompressible BV vector fields in 2D},
number = {SISSA;67/2014/MATE},
year = {2014},
institution = {SISSA},
abstract = {Given a bounded autonomous vector field $b \colon \R^d \to \R^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*}
We are interested in the case where $b$ is of class BV and it is nearly incompressible.
Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio{\textquoteright}s superposition principle [4].},
url = {http://urania.sissa.it/xmlui/handle/1963/7483},
author = {Stefano Bianchini and Paolo Bonicatto and N.A. Gusev}
}