Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality

Abstract

We prove that the Dean-Kawasaki SPDE admits a solution only in integer parameter regimes, in which case the solution is given in terms of non-interacting particles.

References in corpus (8)

• Macroscopic fluctuation theory
• Equilibrium dynamics of the Dean-Kawasaki model: MCT and beyond
• Pattern formation with repulsive soft-core interactions: discrete particle dynamics and Dean-Kawasaki equation
• On the Brownian gas: a field theory with a Poissonian ground state
• Computing diffusivities from particle models out of equilibrium
• Geometrical interpretation of fluctuating hydrodynamics in diffusive systems
• A Lack of Ricci Bounds for the Entropic Measure on Wasserstein space over the Interval
• Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

Cited by in corpus (2)

• A priori positivity of solutions to a non-conservative stochastic thin-film equation
• Numerical approximation of singular-degenerate parabolic stochastic PDEs