My main research interests are the following.
- Mathematical questions related to propagation and interaction of waves in incompressible fluid dynamics. Such waves are often anisotropic and typically involve homogeneous operators of degree 0, like (composition of) the Riesz transform. They are currently the subject of several studies in oceanography and experimental fluid dynamics.
- Stability and instability of special solutions in fluid-dynamics problem. Stability mechanisms can typically involve (partial or full) viscosity/friction or mixing (inviscid damping).
- The interplay of partial dissipation, anisotropy and special nonlinear structure and its impact on the time evolution of solutions to hyperbolic and dispersive systems.
- Singular perturbation systems arising the modeling of shallow-water fluids and congestion phenomena (including traffic congestion).
I typically use tools from the general theory of PDE such as Fourier analysis (including pseudo/paradifferential calculus), methods for hyperbolic PDEs (including front-tracking in BV), boundary layer theory, singular perturbation methods. Although it is not one of my main research lines, I am also interested in numerical analysis with application to fluid-dynamics problems.
In one sentence, one could say that my main interests are focused on PDEs, Fourier analysis and numerical analysis, with special enthusiasm in fluid-dynamics problems, where a combination of those succeeds.
Link to the personal webpage: Pagina personale