82 citations · 147 across the 21 of their papers we have counts for
7 papers · 1 filter
Unbounded rough drivers, rough PDEs and applications
Antoine Hocquet, Martina Hofmanova, Torstein Nilssen
A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present…
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…
Random dynamical system generated by the 3D Navier-Stokes equation with rough transport noise
Jorge Cardona, Martina Hofmanova, Torstein Nilssen +1
We consider the Navier-Stokes system in three dimensions perturbed by a transport noise which is sufficiently smooth in space and rough in time. The existence of a weak solution wa…
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…
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
Andris Gerasimovics, Antoine Hocquet, Torstein Nilssen
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_…
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…