Research Interests

  I am an applied mathematician working on problems that arise in fluid dynamics. I am interested in systems involving immiscible fluids that are characterised by the presence of spatiotemporally evolving sharp interfaces. To obtain a quantitative description of the dynamics we need to determine moving interfaces as part of the solution. Such problems are of much practical importance but are notoriously difficult mathematically for several reasons:
  1. The Navier-Stokes (or Stokes or Euler) equations need to be solved in changing domains.
  2. In certain applications we may need to also solve for the temperature or electrostatic fields.
  3. Several nonlinear boundary conditions need to be specified at the unknown interface(s). These are
  4. The solutions may not exist for all times. In fact we can encounter singularities in finite time accompanied by topological transitions. A simple example is the breakup of liquid jets.
I use a combination of modelling, analysis and computations to gain a quantitative understanding of the underlying nonlinear mechanisms in multi-fluid flows at different length-scales.