26 citations · 36 across the 15 of their papers we have counts for
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Global existence of weak solutions to a two-phase diffuse interface model of ferrofluids dynamics
Samuel Lanthaler, Franziska Weber
Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded d…
On the vanishing viscosity limit of statistical solutions of the incompressible Navier-Stokes equations
Ulrik Skre Fjordholm, Siddhartha Mishra, Franziska Weber
We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are pr…
On Bayesian data assimilation for PDEs with ill-posed forward problems
Samuel Lanthaler, Siddhartha Mishra, Franziska Weber
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Na…
Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Sam Punshon-Smith +1
We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales f…
On the dynamics of ferrofluids: Global weak solutions to the Rosensweig system and rigorous convergence to equilibrium
Ricardo H. Nochetto, Konstantina Trivisa, Franziska Weber
This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics of ferrofluids. The syste…
A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Samuel Punshon-Smith +1
We prove that statistically stationary martingale solutions of the 3D Navier-Stokes equations on subjected to white-in-time (colored-in-space) forcing satisfy the Ko…