Lucio Galeati

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20242026

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math.AP2025

Almost-everywhere uniqueness of Lagrangian trajectories for $3$ D Navier--Stokes revisited

Lucio Galeati

We show that, for any Leray solution $u$ to the $3$ D Navier--Stokes equations with $u_{0} \in L^{2}$ , the associated deterministic and stochastic Lagrangian trajectories are unique for…

math.AP2025

On the well-posedness of (nonlinear) rough continuity equations

Lucio Galeati, James-Michael Leahy, Torstein Nilssen

Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-…

Almost-everywhere uniqueness of Lagrangian trajectories for 3D Navier--Stokes revisited

On the well-posedness of (nonlinear) rough continuity equations

Almost-everywhere uniqueness of Lagrangian trajectories for $3$ D Navier--Stokes revisited