Abstract:On August 8, 1900, David Hilbert delivered his famous lecture about 23 open mathematical problems at the second International Congress of Mathematicians in Paris. This influenced the decision of a recently formed Clay Mathematical Institute (CMI) to announce the seven Millennium Prize Problems in the CMI Millennium Meeting held on May 24, 2000. One such problem is the theme of the present talk. Now it is widely accepted that the motion of an incompressible viscous fluid with moderate velocity is described by the Navier-Stokes Equations. Although these equations were written down in the 19th century, the existing mathematical results are not adequate to unfold the secrets hidden in the Navier-Stokes equations. In this talk, I shall concentrate on:
- a brief description of this problem
- mathematical model
- a quick look at history
- what is known at this point
- some important approaches
- What is possibly needed
Finally, I conclude the talk with a note on the present state of Indian applied mathematics and whether we are ready to contribute towards this millennium problem.