Renormalization for autonomous nearly incompressible BV vector fields in 2D

created by bonicatto on 20 Dec 2014
modified on 04 Nov 2015

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Submitted Paper

Inserted: 20 dec 2014
Last Updated: 4 nov 2015

Year: 2014

Abstract:

Given a bounded autonomous vector field $b \colon \mathbb R^d \to \mathbb R^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation $\partial_t u + b \cdot \nabla u= 0.$ 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.