21 citations · 25 across the 9 of their papers we have counts for
10 papers
Fluctuation dynamics in randomly advected Navier-Stokes equations below critical scaling
Arnaud Debussche, Martina Hofmanová
We study randomly advected incompressible Navier-Stokes equations, where the advecting field is a mean-zero, divergence-free, space-time stationary velocity field with smooth order…
Non-uniqueness of mild solutions to supercritical heat equations
Irfan Glogić, Martina Hofmanová, Theresa Lange +1
We consider the focusing power nonlinearity heat equation \begin{equation}\label{Eq:Heat_abstract}\tag{NLH} \partial_t u -Δu = |u|^{p-1}u, \quad p>1, \end{equation} in dimensions $…
Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
We consider stochastic forced Navier--Stokes equations on starting from zero initial condition. The noise is linear multiplicative and the equations are perturbed…
Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise
Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu +1
We consider a family of singular surface quasi-geostrophic equations on $[0,\infty)…
Rough analysis of two scale systems
Arnaud Debussche, Martina Hofmanová
We address a slow-fast system of coupled three dimensional Navier--Stokes equations where the fast component is perturbed by an additive Brownian noise. By means of the rough path…
Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions
Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana
We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we…
Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations
Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu +1
We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field sati…
Kolmogorov law for the forced 3D Navier-Stokes equations
Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu +1
We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an -in-time version of the Kolmogorov 4/5 law for the behavior of th…
Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
Martina Hofmanová, Theresa Lange, Umberto Pappalettera
We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions c…
Can probability theory really help tame problems in mathematical hydrodynamics?
Martina Hofmanová, Florian Bechtold
Recent years have seen spectacular progress in the mathematical study of hydrodynamic equations. Novel tools from convex integration in particular prove extremely versatile in esta…