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Linear transport and ODEs for weakly regular vector fields

Lecturer

Stefano Bianchini, SISSA

Location

601 Pao Yue-Kong Library

Time

Abstract

These lectures concern the PDEs of linear transport (in conservative or advective form)

\begin{equation} \partial_t \rho + \dive (\rho \mathbf b) = 0, \quad u_t + \mathbf b \cdot \nabla u = 0, \end{equation}

and their relations with the ODE

\begin{equation} \frac{d}{dt} x = \mathbf b(t,x). \end{equation}

The aim is to show that as in the classical/regular case, a synergy between the two formulations allows to develop an advanced theory about flows generated by weakly regular vector fields.

We will try to cover the following subjects: