Department of Mathematics
Title : Singularities in fluid mechanics: a grand challenge
| Speaker: Prof. Jim Denier Affiliation: University of Auckland Time: 2:00 pm Thursday, 1 November, 2012 Location: Room 301-242 (Seminar Room 242, Building 301 (Chemistry Building) |
Abstract
| We've all heard about the seven Clay Millennium Prize problems which have a $1M prize awaiting the first person to provide a solution. One of these is the Navier-Stokes Equation which is concerned with the existence and uniqueness of solutions to the Navier-Stokes equations, first written by Claude-Louis Navier and George Gabriel Stokes in the 19th century. Hidden within this prize problem is the question of whether there are solutions to the Navier-Stokes equations which are singular. Many applied mathematicians believe that there are singular solutions, but a definite proof evades us to this day. In this talk I'll consider a number of problems where the mathematical exploration of a description of the flow of fluids does lead to singular behaviour and explore some of the structure of these singularities. Alas, the solutions that I'll describe aren't going to win me (or anyone else) the $1M prize as they are solutions to reduced equations based upon the Navier-Stokes equations. They will however, serve to explain the importance of the prize problem and why we might be interested in it. A mathematical description of the Navier-Stokes problem can be found at www.claymath.org/millennium/Navier-Stokes_Equations/ and a layman's description at theconversation.edu.au/millennium-prize-the-navier-stokes-existence-and-uniqueness-problem-4244 |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
