59 citations · 193 across the 23 of their papers we have counts for
34 papers
Compressible fluids excited by space-dependent transport noise
D. Breit, E. Feireisl, M. Hofmanova +1
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is…
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…
A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity
Martina Hofmanova, Rongchan Zhu, Xiangchan Zhu
We study the surface quasi-geostrophic equation with an irregular spatial perturbation on $…
Compressible Navier--Stokes system with transport noise
Dominic Breit, Eduard Feireisl, Martina Hofmanova +1
We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both continuity as well as momentum equation. We focus on three different…
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…
Randomness in compressible fluid flows past an obstacle
Eduard Feireisl, Martina Hofmanova
We consider a statistical limit of solutions to the compressible Navier--Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to wh…
On the long time behavior of compressible fluid flows excited by random forcing
Dominic Breit, Eduard Feireisl, Martina Hofmanova
We are concerned with the long time behavior of the stochastic Navier--Stokes system for compressible fluids in dimension two and three. In this setting, the part of the phase spac…
Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits
Martina Hofmanova, Ujjwal Koley, Utsab Sarkar
We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.…
Generalized solutions to models of inviscid fluids
Dominic Breit, Eduard Feireisl, Martina Hofmanova
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Eu…
Space-time approximation of stochastic -Laplace systems
Dominic Breit, Martina Hofmanova, Sebastien Loisel
We consider systems of stochastic evolutionary equations of the -Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the erro…
Dissipative solutions and semiflow selection for the complete Euler system
Dominic Breit, Eduard Feireisl, Martina Hofmanova
To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant so…
Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs
Nils Dabrock, Martina Hofmanová, Matthias Röger
We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. We establish existence of martingale solutions which are strong in t…
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
Martina Hofmanova, James-Michael Leahy, Torstein Nilssen
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…
Solution semiflow to the isentropic Euler system
Dominic Breit, Eduard Feireisl, Martina Hofmanova
It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill--posed. Even certain smooth initial data give rise to infinitely many solutions…
A PDE construction of the Euclidean quantum field theory
Massimiliano Gubinelli, Martina Hofmanova
We present a new construction of the Euclidean quantum field theory on based on PDE arguments. More precisely, we consider an approximation of the stochastic q…
Markov selection for the stochastic compressible Navier--Stokes system
Dominic Breit, Eduard Feireisl, Martina Hofmanova
We analyze the Markov property of solutions to the compressible Navier--Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost s…
Global solutions to elliptic and parabolic models in Euclidean space
Massimiliano Gubinelli, Martina Hofmanová
We prove existence of global solutions to singular SPDEs on with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensio…
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…
On the rough Gronwall lemma and its applications
Martina Hofmanova
We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanová, S. Tindel in [arXiv:1604.00437] and discuss two of its ap…
On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
Dominic Breit, Eduard Feireisl, Martina Hofmanova
We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show t…
Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces
Dominic Breit, Eduard Feireisl, Martina Hofmanova +1
We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicati…
One-dimensional reflected rough differential equations
Aurelien Deya, Massimiliano Gubinelli, Martina Hofmanova +1
We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the la…
Local strong solutions to the stochastic compressible Navier-Stokes system
Dominic Breit, Eduard Feireisl, Martina Hofmanova
We study the Navier-Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence…
An exponential-type integrator for the KdV equation
Martina Hofmanova, Katharina Schratz
We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in for initial data in . Furthermore, we outline the generali…