Research
My research concerns nonlinear partial differential equations and mathematical fluid dynamics. I investigate conditions that prevent singularity formation in three-dimensional classical and hyperdissipative Navier–Stokes flows.
Hyperdissipative Analyticity and Sparseness
For hyperdissipative Navier–Stokes systems below the Lions threshold, I study how bounds on derivative ratios connect the radius of spatial analyticity to the geometric sparseness of regions of intense fluid activity. Time-weighted bridge inequalities, combined with harmonic-measure estimates, yield conditional criteria excluding classes of finite-time blow-up scenarios.
Read the paper · Journal of Mathematical Fluid Mechanics (2026)
Classical Navier–Stokes Derivative Bridges
In joint work with Zoran Grujić, I investigate time-weighted inequalities relating lower- and higher-order derivative norms in the classical Navier–Stokes equations. These inequalities allow a comparison between analyticity and sparseness scales; under the stated assumptions, that comparison rules out a class of strongly turbulent blow-up scenarios.
Read the preprint · arXiv (2026)
Methods and Themes
- Spatial analyticity and higher-order derivative estimates
- Geometric sparseness and harmonic-measure methods
- Regularity criteria and higher-order turbulence scales