26 citations · 50 across the 11 of their papers we have counts for
4 papers · 1 filter
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-…
Solution properties of the incompressible Euler system with rough path advection
Dan Crisan, Darryl D. Holm, James-Michael Leahy +1
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressi…
Variational principles for fluid dynamics on rough paths
Dan Crisan, Darryl D. Holm, James-Michael Leahy +1
In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynami…
On the Navier-Stokes equation perturbed by rough transport noise
Martina Hofmanová, James-Michael Leahy, Torstein Nilssen
We consider the Navier-Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing th…