## Summary

John has been in the Imperial Mathematics Department since September 1980. His research interests lie in the study of turbulence in fluid dynamics from a mainly mathematical perspective. One of the major unsolved problems of modern applied mathematics concerns the regularity of solutions of the 3D incompressible Navier-Stokes equations. Related to this is the behaviour of solutions of the incompressible 3D Euler equations. Both problems, and particularly the former, suggest that vorticity clusters on fractal-like sets. The aim is to provide a general theory of this phenomenon which has applications to many areas of physics & applied mathematics.

John Gibbon's personal webpage can be found at http://www.ma.ic.ac.uk/~jdg/

## Selected Publications

### Journal Articles

Gibbon JD, 2012, A HIERARCHY OF LENGTH SCALES FOR WEAK SOLUTIONS OF THE THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS, *Communications in Mathematical Sciences*, Vol:10, ISSN:1539-6746, Pages:131-136