for this workshop
Mixing and nonlinear stability
at the
American Institute of Mathematics, San Jose, California
organized by
Jacob Bedrossian and Nader Masmoudi
This workshop, sponsored by AIM and the NSF, will be devoted to expanding the mathematical analysis of mixing phenomena arising in fluid mechanics and kinetic theory as well as increasing communication between the different communities working in the field. The specific focus will be on the relationship between mixing and nonlinear stability problems, that is, how the fluid mixing itself changes the dynamics. In fluid mechanics, mixing-related stability mechanisms are connected to coherent structures at high Reynolds number and thought to be important for understanding the stability of hurricanes and other weather phenomena as well as potentially playing a role in organizing 2D turbulence. Recent work also shows that these effects are important for understanding the stability and subcritical instability of 3D laminar flows. In plasma physics and galaxy dynamics, the mixing effect known as Landau damping has long been recognized as a fundamental stability mechanism in nearly collisionless kinetic models. Despite its fundamental physical relevance and importance in practical settings, the mathematical analysis of these mixing phenomena is very under-developed due to subtle regularity issues connected with unusual nonlinear resonances and even often a lack of clear understanding of linear mixing phenomena.
The main topics of interest will likely cover:
- Understanding general pseudospectral aspects of associated linear operators, with both zero and vanishingly small viscosity (or collisions). Especially we will focus on aspects important for nonlinear problems.
- Relevance to understanding the meta-stability of coherent structures in 2D fluids, understanding subcritical transition phenomena in 3D laminar flows, and to understanding similar phenomena in plasma physics.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
For more information email workshops@aimath.org
