Research Interests

Research Interests

Analyzing possible singularity formation in nonlinear partial differential equations arising as models in 3D incompressible fluid and plasma dynamics. Mathematical theory of turbulent cascades and turbulent dissipation in 3D flows.

Leonardo

Of particular interest has been the study of formation of small scales and turbulent dissipation in 3D Navier-Stokes (NS) equations within a mathematical framework based on the suitably defined `scale of sparseness' of the regions of intense fluid activity. Specifying this framework to the super-level sets of the positive and negative parts of the components of the higher-order spatial derivatives revealed asymptotically critical nature of the NS regularity problem arXiv--and more recently--criticality of the Navier-Stokes diffusion in a turbulent scenario arXiv.