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math.AP2026
Delayed Dissipation for Two-Dimensional Vortex Sheets
Victor Armegioiu
We quantify viscous energy loss for two-dimensional Delort vortex sheets. Let be Leray-Hopf solutions on with uniformly bounded kinetic energy and total vorti…
math.AP2026
The Semigeostrophic--Euler Limit via Perturbative Monge--Ampère Estimates
Victor Armegioiu
We study the two-dimensional semigeostrophic system on the flat torus in the small-amplitude regime. We formulate the rescaled dynamics as the Lie--Poisson flow of a renormalized o…
math.AP2026
Statistical Error Bounds for Generative Solvers of Chaotic PDEs: Wasserstein Stability, Generalization, and Turbulence
Victor Armegioiu
Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on whose multi-point correlations satisfy an infinite hierarchy of weak i…