Analyticity in time and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional, compressible flow

Series: 
PDE Seminar
Tuesday, August 25, 2009 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
Indiana University, Bloomington
We prove that solutions of the Navier-Stokes equations of three-dimensional, compressible flow, restricted to fluid-particle trajectories, can be extended as analytic functions of complex time. One important corollary is backwards uniqueness: if two such solutions agree at a given time, then they must agree at all previous times. Additionally, analyticity yields sharp estimates for the time derivatives of arbitrary order of solutions along particle trajectories. I'm going to integrate into the talk something like a "pretalk" in an attempt to motivate the more technical material and to make things accessible to a general analysis audience.