Research Interests
My research interests are mathematical modelling and methods, numerical analysis and scientific computing around nonlinear PDEs which arise in plasma physics and fluid mechanics:
- Nonlinear Vlasov equations (charged particles transport processes, electromagnetic versus gravitational interactions)
- Geometric reduction of Vlasov equations by geometric Liouville invariants (waterbags type models, multi–fluids models)
- Quasilinear theory, models for plasma turbulence (Hamiltonian versus dissipative, resonant wave–particle interaction)
- Hydrodynamics and Magneto–Hydrodynamics models (Incompressible Euler equations, MHD, XMHD)
- Semi-classical limits of nonlinear Schrödinger equations (WKB, singular interaction potential)
- New (deterministic & stochastic) Lagrangian formulation of fluid mechanics on flat and curved spaces
- Geometric Lagrangian formulation of fluid mechanics with applications for mathematical and numerical analysis
- Numerical schemes of arbitrary high order for fluid mechanics with applications for finite-time singularities (blowup)
