Regularity, singularity and well-posedness of some mathematical models in physics

When
Start: 03/10/2010 - 4:15pm
End  : 03/10/2010 - 5:15pm

Category
Colloquium

Speaker
Saleh Tanveer, Ohio State University

Abstract

Description of a physical phenomenon through a mathematical model invariably involves dropping some terms that are considered negligible. Nonetheless, a simplified model must have some mathematical properties in order to faithfully model the physics. These include regularity and well-posedness. Regularity refers to solution being sufficiently smooth. The concept of well-posedness includes existence, uniqueness and continuous dependence on initial data and boundary data in an appropriate norm. Singularities in a solution suggest that terms ignored in a model can be important--this has immediate consequence on the smallest predicted scales seen in experiments. A mathematical problem which is not well posed cannot be physically relevant since, in the real world, we can only know initial and boundary conditions to finite precision. When a small regularizing term is included in an otherwise unstable model, the near structural instability can manifest itself in the highly unusual phenomena where disparate length scales interact. We will illustrate these notions through a series of examples from fluid mechanics and other physical problems.

Where
Beckman B126, Harvey Mudd College

Misc. Information

Coffee & Cookies at 3:45 pm in Olin B161 Harvey Mudd College
The dinner will be hosted by Professor Adolfo Rumbos
If interested in attending, please call ext 18713