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

- Series
- PDE Seminar
- Time
- Tuesday, August 25, 2009 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- David Hoff – 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.