4 papers
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…
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…
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…
Memory-Conditioned Flow-Matching for Stable Autoregressive PDE Rollouts
Victor Armegioiu
Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved f…