6 papers
A new reduced order model of linear parabolic PDEs
Noel Walkington, Franziska Weber, Yangwen Zhang
How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for…
Well-posedness of Bayesian inverse problems for hyperbolic conservation laws
Siddhartha Mishra, David Ochsner, Adrian M. Ruf +1
We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (po…
A convergent numerical scheme for a model of liquid crystal dynamics subjected to an electric field
Franziska Weber
We present a convergent and constraint-preserving numerical discretization of a mathematical model for the dynamics of a liquid crystal subjected to an electric field. This model c…
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…