Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality
Probability
2018-06-14 v1
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.
Cite
@article{arxiv.1806.05018,
title = {Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality},
author = {Tobias Lehmann and Vitalii Konarovskyi and Max-K. von Renesse},
journal= {arXiv preprint arXiv:1806.05018},
year = {2018}
}
Related papers
View all related →
Probability · Mathematics
Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
Ana Djurdjevac, Helena Kremp, Nicolas Perkowski
2024-06-21
Probability · Mathematics
On Dean-Kawasaki Dynamics with Smooth Drift Potential
Vitalii Konarovskyi, Tobias Lehmann, Max von Renesse
2020-10-21
Probability · Mathematics
Dean-Kawasaki equation with initial condition in the space of positive distributions
Vitalii Konarovskyi, Fenna Müller
2024-10-31
Probability · Mathematics
Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions
Ana Djurdjevac, Xiaohao Ji, Nicolas Perkowski
2025-03-03
Probability · Mathematics
Surface Dean--Kawasaki equations
John Bell, Ana Djurdjevac, Nicolas Perkowski
2026-05-21
Mathematical Physics · Physics
A non-linear kinetic model of self-propelled particles with multiple equilibria
Paolo Buttà, Franco Flandoli, Michela Ottobre, Boguslaw Zegarlinski
2022-04-11
Analysis of PDEs · Mathematics
Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions
Federico Cornalba, Tony Shardlow, Johannes Zimmer
2021-02-10
Numerical Analysis · Mathematics
A Hybrid Algorithm for Systems of Non-interacting Particles with an External Potential
Ana Djurdjevac, Ann Almgren, John Bell
2025-11-26
Probability · Mathematics
Stochastic PDEs with correlated, non-stationary Stratonovich noise of Dean--Kawasaki type
Benjamin Fehrman
2025-04-28
Probability · Mathematics
From weakly interacting particles to a regularised Dean--Kawasaki model
Federico Cornalba, Tony Shardlow, Johannes Zimmer
2019-09-10
Probability · Mathematics
Unbiased simulation of Asian options
Bruno Bouchard, Xiaolu Tan
2025-11-03
Probability · Mathematics
A regularised Dean-Kawasaki model: derivation and analysis
Federico Cornalba, Tony Shardlow, Johannes Zimmer
2019-01-23
Numerical Analysis · Mathematics
Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor
Xun Tang, Lexing Ying
2026-02-06
Exactly Solvable and Integrable Systems · Physics
Integrability of differential equations with fluid mechanics application: from Painleve property to the method of simplest equation
Zlatinka I. Dimitrova, Kaloyan N. Vitanov
2013-02-05
Probability · Mathematics
Solving McKean-Vlasov SDEs via relative entropy
Yi Han
2025-04-28
Analysis of PDEs · Mathematics
On the Well-posedness of a Class of Non-Autonomous SPDEs: An Operator-Theoretical Perspective
Rainer Picard, Sascha Trostorff, Marcus Waurick
2018-09-03
Probability · Mathematics
On non-negative solutions of SDDEs with an application to CARMA processes
Mikkel Slot Nielsen, Victor Rohde
2020-10-19
Probability · Mathematics
Path-dependent equations and viscosity solutions in infinite dimension
Andrea Cosso, Salvatore Federico, Fausto Gozzi, Mauro Rosestolato +1
2017-03-07
Mathematical Physics · Physics
Peakon-antipeakon interactions in the Degasperis-Procesi Equation
Jacek Szmigielski, Lingjun Zhou
2013-01-07
Probability · Mathematics
Large deviation properties of weakly interacting processes via weak convergence methods
Amarjit Budhiraja, Paul Dupuis, Markus Fischer
2012-09-26
Optimization and Control · Mathematics
Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem without Monotonicity Condition
Said Hamadène, Mohamed Mnif, Sarah Neffati
2018-02-14
Systems and Control · Electrical Eng. & Systems
Reformulation of Matching Equation in Potential Energy Shaping
M. Reza J. Harandi, Hamid D. Taghirad
2021-12-17
Statistical Mechanics · Physics
A generalized Dean-Kawasaki equation for an interacting Brownian gas in a partially absorbing medium
Paul C Bressloff
2023-12-12
Classical Analysis and ODEs · Mathematics
Painleve Test and the Resolution of Singularities for Integrable Equations
Jishan Hu, Min Yan
2013-05-01
Analysis of PDEs · Mathematics
A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Declan S. Jagt, Matthew M. Peet
2026-05-20