[LLIBRE][B] A course on rough paths

PK Friz, M Hairer - 2020 - Springer
Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

Weak well-posedness by transport noise for a class of 2D fluid dynamics equations

L Galeati, D Luo - arxiv preprint arxiv:2305.08761, 2023 - arxiv.org
A fundamental open problem in fluid dynamics is whether solutions to $2 $ D Euler
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …

On Ill‐and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations

M Hofmanová, R Zhu, X Zhu - Communications on Pure and …, 2022 - Wiley Online Library
We are concerned with the question of well‐posedness of stochastic, three‐dimensional,
incompressible Euler equations. In particular, we introduce a novel class of dissipative …

Dynamical heterogeneities close to a colloidal gel

AM Puertas, M Fuchs, ME Cates - The Journal of chemical physics, 2004 - pubs.aip.org
Dynamical heterogeneities in a colloidal fluid close to gelation are studied by means of
computer simulations. A clear distinction between some fast particles and the rest, slow …

On the Navier–Stokes equation perturbed by rough transport noise

M Hofmanová, JM Leahy, T Nilssen - Journal of Evolution Equations, 2019 - Springer
Abstract 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 …

[HTML][HTML] Variational principles for fluid dynamics on rough paths

D Crisan, DD Holm, JM Leahy, T Nilssen - Advances in Mathematics, 2022 - Elsevier
In recent works, beginning with [76], several stochastic geophysical fluid dynamics (SGFD)
models have been derived from variational principles. In this paper, we introduce a new …

Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma

A Gerasimovičs, A Hocquet, T Nilssen - Journal of Functional Analysis, 2021 - Elsevier
We investigate existence, uniqueness and regularity for local solutions of rough parabolic
equations with subcritical noise of the form dut− L tutdt= N (ut) d t+∑ i= 1 d F i (ut) d X ti …

On a rough perturbation of the Navier–Stokes system and its vorticity formulation

M Hofmanová, JM Leahy, T Nilssen - 2021 - projecteuclid.org
We introduce a rough perturbation of the Navier–Stokes system and justify its physical
relevance from balance of momentum and conservation of circulation in the inviscid limit. We …

Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field

F Flandoli, M Hofmanová, D Luo… - The Annals of Applied …, 2022 - projecteuclid.org
We are concerned with the problem of global well-posedness of the 3D Navier–Stokes
equations on the torus with unitary viscosity. While a full answer to this question seems to be …

[HTML][HTML] An energy method for rough partial differential equations

A Hocquet, M Hofmanová - Journal of Differential Equations, 2018 - Elsevier
We present a well-posedness and stability result for a class of nondegenerate linear
parabolic equations driven by geometric rough paths. More precisely, we introduce a notion …