We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion
with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We …

We show that generic H\" older continuous functions are $\rho $-irregular. The property of
$\rho $-irregularity has been first introduced by Catellier and Gubinelli (Stoc. Proc. Appl …

We study an evolutionary p-Laplace problem whose potential is subject to a translation in
time. Provided the trajectory along which the potential is translated admits a sufficiently …

We consider the rough differential equation with drift driven by a Gaussian geometric rough
path. Under natural conditions on the rough path, namely nondeterminism, and uniform …

In this work, we pursue our investigations on the Cauchy problem for a class of dispersive
PDEs where a rough time coefficient is present in front of the dispersion. We show that if the …

In this work, we study the Cauchy problem for a class of dispersive PDEs where a rough time
coefficient is present in front of the dispersion. Under minimal assumptions on the …

We establish a multiparameter extension of the stochastic sewing lemma. This allows us to
derive novel regularity estimates on the local time of locally non-deterministic Gaussian …

(Due to the limit on the number of characters for an abstract set by arxiv, the full abstract can
not be displayed here. See the abstract in the paper.) We study dispersive equations with a …

This thesis concerns the study of regularisation by noise phenomena for ODEs and PDEs. In
particular, it focuses on the use of so called pathwise techniques: our aim is to identify …

In the context of ODEs or transport PDEs, there are examples where adding a rough
stochastic perturbation to the equation at hand actually improves the well-posedness theory …