Seminars & Events for Analysis of Fluids and Related Topics

September 21, 2017
4:30pm - 5:30pm
Global well-posedness for the 2D Muskat problem

The Muskat problem was originally introduced by Muskat in order to model the interface between water and oil in tar sands. In general, it describes the interface between two incompressible, immiscible fluids of different constant densities in a porous media. In this talk I will prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the initial data is monotonic or has slope strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$ goes to infinity, and they are unique when the initial data is $C^{1,\epsilon}$. We do this by constructing a modulus of continuity generated by the equation, just as Kiselev, Naverov, and Volberg did in their proof of the global well-posedness for the quasi-geostraphic equation.

Speaker: Stephen Cameron, University of Chicago
Location:
Fine Hall 322
September 28, 2017
4:30pm - 5:30pm
TBA-Minh Binh Tran
Speaker: Minh Binh Tran, University of Wisconsin
Location:
Fine Hall 322
October 5, 2017
4:30pm - 5:30pm
TBA-Sam Punshon-Smith
Speaker: Sam Punshon-Smith , University of Maryland
Location:
Fine Hall 322
October 12, 2017
4:30pm - 5:30pm
The optimal design of wall-bounded heat transport

Flowing a fluid is a familiar and efficient way to cool: fans cool electronics, water cools nuclear reactors, and the atmosphere cools the Earth. In this talk, we discuss a class of problems from fluid dynamics concerning the design of incompressible wall-bounded flows achieving optimal rates of heat transport for a given flow intensity budget. Guided by a perhaps unexpected connection between this optimal design problem and various “energy-driven pattern formation” problems from materials science, we construct flows achieving nearly optimal rates of heat transport in their scaling with respect to the intensity budget. The resulting flows share striking similarities with self-similar elastic wrinkling patterns, such as can be seen in the shape of a hanging drape or nearby the edge of a torn plastic sheet.

Speaker: Ian Tobasco, University of Michigan
Location:
Fine Hall 322
October 19, 2017
4:30pm - 5:30pm
TBA-Alexei Mailybaev
Speaker: Alexei Mailybaev , Nacional de Matemática Pura e Aplicada (IMPA)
Location:
Fine Hall 322
October 26, 2017
4:30pm - 5:30pm
TBA-Jens Eggers
Speaker: Jens Eggers , University of Bristol
Location:
Fine Hall 322
November 16, 2017
3:30pm - 4:30pm
TBA-Mimi Dai
Speaker: Mimi Dai , University of Illinois at Chicago
Location:
Fine Hall 322
November 30, 2017
4:30pm - 5:30pm
TBA-Serguei Denissov
Speaker: Serguei Denissov, University of Wisconsin
Location:
Fine Hall 322
December 7, 2017
4:30pm - 5:30pm
TBA-Gautam Iyer
Speaker: Gautam Iyer, Carnegie Mellon University
Location:
Fine Hall 322