90 citations · 178 across the 11 of their papers we have counts for
17 papers
Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
We establish the existence of infinitely many stationary solutions, as well as ergodic stationary solutions, to the three dimensional Navier--Stokes and Euler equations in both det…
An averaged space-time discretization of the stochastic -Laplace system
Lars Diening, Martina Hofmanová, Jörn Wichmann
We study the stochastic -Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linea…
Weak solutions for singular multiplicative SDEs via regularization by noise
Florian Bechtold, Martina Hofmanová
We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we esta…
Global existence and non-uniqueness for 3D Navier--Stokes equations with space-time white noise
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In t…
Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initia…
Stationary solutions in thermodynamics of stochastically forced fluids
Dominic Breit, Eduard Feireisl, Martina Hofmanová
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system i…
On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
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 soluti…
Ergodic theory for energetically open compressible fluid flows
Francesco Fanelli, Eduard Feireisl, Martina Hofmanová
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We s…
Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field
Franco Flandoli, Martina Hofmanová, Dejun Luo +1
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…
Non-uniqueness in law of stochastic 3D Navier--Stokes equations
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
We consider the stochastic Navier--Stokes equations in three dimensions and prove that the law of analytically weak solutions is not unique. In particular, we focus on three exampl…
On convergence of approximate solutions to the compressible Euler system
Eduard Feireisl, Martina Hofmanová
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vani…
Randomized exponential integrators for modulated nonlinear Schrödinger equations
Martina Hofmanová, Marvin Knöller, Katharina Schratz
We consider the nonlinear Schrödinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class …
An energy method for rough partial differential equations
Antoine Hocquet, Martina Hofmanová
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak soluti…
Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
Benjamin Gess, Martina Hofmanová
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our resu…
A priori estimates for rough PDEs with application to rough conservation laws
Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanová +1
We introduce a general weak formulation for PDEs driven by rough paths, as well as a new strategy to prove well-posedness. Our procedure is based on a combination of fundamental a…
Stochastic Navier-Stokes equations for compressible fluids
Dominic Breit, Martina Hofmanová
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we cons…
Degenerate parabolic stochastic partial differential equations: Quasilinear case
Arnaud Debussche, Martina Hofmanová, Julien Vovelle
In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we…