Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, February 29, 2016 - 16:00 to 17:00
Location: 
Kidder 350

Speaker Info

Institution: 
The University of Michigan
Abstract: 

Optimization and optimal dynamical control are used to investigate the accuracy of analytical estimates for solutions of some basic nonlinear partial differential equations of mathematical hydrodynamics. Even though many mathematical estimates are demonstrably sharp, the result of a sequence of applications of such estimates need not be sharp leaving uncertainty in the ultimate result of the analysis. We examine the classical analysis bounding enstrophy and palinstrophy amplification in Burgers? and the Navier-Stokes equations and discover that the best known instantaneous growth rates estimates are indeed sharp. But integrating the estimates in time produces bounds that are not always sharp. When they are not, optimal control techniques must be brought to bear to determine the actual extreme behavior of the nonlinear dynamics. The question of 3D Navier-Stokes regularity remains unanswered although work is in progress to apply these tools to this challenge.