Mr. Amsaad Mohamed 5/7/2012

Well-posedness Theory of the Transport Equation

Date: 5/7/2012
Time: 11:30AM-12:30 PM
Place: 315 Armstrong Hall

In this talk, first we
will try to introduce the connection between the ordinary differential
equation(ODE) and the transport equation under some regularity assumptions
on the vector field. We will start by recalling the classical results of
the Cauchy-Lipschitz theory (in which Lipschitz regularity of the vector
field is assumed) and then will present some ideas of the theory of
characteristics and the connection between the ODE and the transport and
the continuity equations in the smooth case. Next, we will begin to
investigate the well-posedness of the transport equation out of the smooth
setting and then we will illustrate the importance of the notion of
renormalization property and how this property implies well-posedness of
the transport equation.