3 papers
math.AP2026
On the flexibility of 2D Euler steady states
Tarek M. Elgindi, Yupei Huang
We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown p…
math.AP2025
Absence of anomalous dissipation for vortex sheets
Tarek Elgindi, Milton Lopes Filho, Helena Nussenzveig Lopes
A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of…
math.AP2025
Cusp Formation in Vortex Patches
Tarek M. Elgindi, Min Jun Jo
We prove instantaneous cusp formation for any initial vortex patch with acute corners. This was conjectured to occur in the numerical literature.