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Research Fellows Directory

Steve Shkoller

Professor Steve Shkoller

Research Fellow


University of Oxford

Research summary

In recent work the Research Fellow has developed a novel methodology for analyzing a number of free-boundary and moving interface problems in fluid dynamics, and for multi-D systems of conservation laws with propagating surfaces of discontinuity.

Multiphase fluid flows with moving interfaces play a central role

in a multitude of physical and engineering applications, ranging

from the creation of hurricanes due to wind blowing on top of the

ocean surface to the atomization of liquid fuel jets in combustion

chambers to the motion of astrophysical bodies such as gaseous stars.

The analytical understanding gained in this work may have important

ramifications in the understanding of basic

physical phenomena, which is heretofore, poorly understood. In addition

to basic wave motion and singularities that occurs in the motion of interfaces

between water and air, other conventional examples include the interface

between air and helium under shock wave interaction, the Richtmyer-Meshkov

instabilities between two gases, the behavior of a gas bubble in a liquid in a

shock wave, and liquid fuels which are usually burned by first atomizing a

fuel jet to increase the surface area and hence the evaporation


It is expected that a new set of analysis tools will be developed for moving

boundary PDE in fluids in which the geometric structure of the PDE is crucial

for the control of higher-order energies via a priori estimates. It is believed that these methods will have a broader impact on the general field

of hyperbolic PDE, and in particular geometric PDE and shock wave theory.

The research experience acquired from this project will

be translated into course work spanning mathematics, engineering and

physics disciplines. In particular, teaching modules will

be developed based on this research effort and will be implemented in

various courses for the Center for Doctoral Training in the Analysis of PDE at


Grants awarded

Analysis of moving free-boundary problems in fluid dynamics

Scheme: Wolfson Research Merit Awards

Dates: Sep 2013 - Oct 2014

Value: £62,000