The Dean-Kawasaki equation and stochastic density functional theory
P Illien - arXiv preprint arXiv:2411.13467, 2024 - arxiv.org
The Dean-Kawasaki (DK) equation, which is at the basis of stochastic density functional
theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of …
theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of …
Well-posedness of the Dean–Kawasaki and the nonlinear Dawson–Watanabe equation with correlated noise
B Fehrman, B Gess - Archive for Rational Mechanics and Analysis, 2024 - Springer
In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation
driven by noise that is white in time and colored in space. The results treat diffusion …
driven by noise that is white in time and colored in space. The results treat diffusion …
Dean-Kawasaki dynamics: ill-posedness vs. triviality
V Konarovskyi, T Lehmann, MK von Renesse - 2019 - projecteuclid.org
Electron. Commun. Probab. 24 (2019), no. 8, https://doi.org/10.1214/19-ECP208 Page 1
Electron. Commun. Probab. 24 (2019), no. 8, 1–9. https://doi.org/10.1214/19-ECP208 ISSN …
Electron. Commun. Probab. 24 (2019), no. 8, 1–9. https://doi.org/10.1214/19-ECP208 ISSN …
The Dean–Kawasaki equation and the structure of density fluctuations in systems of diffusing particles
F Cornalba, J Fischer - Archive for Rational Mechanics and Analysis, 2023 - Springer
Abstract The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of
fluctuating hydrodynamics; it has been proposed in the physics literature to describe the …
fluctuating hydrodynamics; it has been proposed in the physics literature to describe the …
Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
The convergence of stochastic interacting particle systems in the mean-field limit to solutions
of conservative stochastic partial differential equations is established, with optimal rate of …
of conservative stochastic partial differential equations is established, with optimal rate of …
On Dean–Kawasaki dynamics with smooth drift potential
V Konarovskyi, T Lehmann, M von Renesse - Journal of Statistical Physics, 2020 - Springer
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[图书][B] Stochastic dynamics in computational biology
S Winkelmann, C Schütte - 2020 - Springer
Computational biology is the science of developing mathematical models and numerical
simulation techniques to understand biological and biochemical systems. Since the early …
simulation techniques to understand biological and biochemical systems. Since the early …
Density fluctuations in weakly interacting particle systems via the dean-kawasaki equation
F Cornalba, J Fischer, J Ingmanns, C Raithel - arXiv preprint arXiv …, 2023 - arxiv.org
The Dean-Kawasaki equation-one of the most fundamental SPDEs of fluctuating
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation
We consider a nonlinear SPDE approximation of the Dean–Kawasaki equation for
independent particles. Our approximation satisfies the physical constraints of the particle …
independent particles. Our approximation satisfies the physical constraints of the particle …
Well-Posedness for Dean-Kawasaki Models of Vlasov-Fokker-Planck Type
F Müller, M von Renesse, J Zimmer - arXiv preprint arXiv:2411.14334, 2024 - arxiv.org
We consider systems of interacting particles which are described by a second order
Langevin equation, ie, particles experiencing inertia. We introduce an associated equation …
Langevin equation, ie, particles experiencing inertia. We introduce an associated equation …