Friday, July 14

Free Boundary Problems

9:15 AM-11:15 AM
Rio Mar 7

Evolution of interfaces in incompressible flow, of surfaces in water waves and of shocks in compressible flow are examples of   free boundary and free surface problems which occur in fluid dynamics applications of partial differential equations. These problems pose both analytical and computational challenges:  the former because there is as yet no   mathematical theory for existence of solutions to standard   formulations of free surface problems when the differential equations are quaslinear;  the latter because specifying fixed grids is usually not effective.  In addition, when the interfaces are unstable, the problem is ill-posed without additional constraints.   In this minisymposium, four speakers will describe how they overcame these difficulties in four problems of current  interest in fluid dynamics.  The approaches include both analytical advances and computational implementations.  We hope to stimulate interaction between researchers using different approaches, and to explore possible extensions. The talks will be of interest to applied analysts, fluid   dynamicists, and computational scientists.

Organizers: Barbara L. Keyfitz
University of Houston and Brown University, USA
Suncica Canic
University of Houston, USA

9:15-9:40 Regular Reflection of Weak Shocks: Existence Proof Using Free-Boundary Approach
Suncica Canic, Organizer
9:45-10:10 Singularity Formation in 3-D Vortex Sheets
Thomas Y. Hou and Gang Hu, California Institute of Technology, USA; and Pingwen Zhang, Peking University, China
10:15-10:40 A New Parturbative Approach to Computing Water Waves
David Nicholls, University of Minnesota, Minneapolis, USA
10:45-11:10 On a Free Boundary Barotropic Model
Nader Masmoudi, Courant Institute of Mathematical Sciences, New York University, USA

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