Event Type:

Analysis Seminar

Date/Time:

Monday, October 24, 2016 - 12:00 to 13:00

Location:

Kidder 356

Local Speaker:

Abstract:

The idea of recasting well-posedness problems for non-linear

parabolic-type PDE in terms of averages of associated multiplicative

cascades goes back to Le Jan and Sznitman's 1997 paper on Navier-Stokes

equation (NSE). More recently, in collaboration with N. Michalowski, E.

Waymire, and E. Thomann, we looked into the connection between uniqueness of

self-symilar (symmetry-preserving) solutions of 3D NSE and uniqueness for

general solutions. In this work we explore these ideas on a much simpler

case of complex Burgers equations. On one hand the probabilistic description

is more explicit allowing us to illustrate the use of such techniques to

study both global existence and uniqueness in a wide scaling-invariant space

as well as to study limit behavior of the solutions. On the other hand, the

multiplicative process itself is non-trivial and further attempts to

simplify it leads to a family of "delayed Yule" processes that may

be of independent interest.