90 citations · 178 across the 11 of their papers we have counts for
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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…
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-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…
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…
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…
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…