On the existence and uniqueness of SDE describing an n-particle system interacting via a singular potential
type: Item
instance of: scholarly article
title: On the existence and uniqueness of SDE describing an n-particle system interacting via a singular potential
zbMATH Open document ID: 0579.60049
author: Satoshi Takanobu
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: The system of the stochastic differential equations describing an interacting n-particle system in \(R^{2d}\) is considered: \[ dZ^ i(t)=\sum_{j:j\neq i}\gamma_ j(\nabla H(Z^ i(t)-Z^ j(t)))^{\perp}dt+d\quad W^ i(t),\quad Z^ i(0)=z^ i,\quad i=1,...,n, \] where \(H(z)=g(| z|)\) \((g\in C^ 2(0,+\infty))\) and \((x,y)^{\perp}=(x,-y)\in R^{2d}\). Under a suitable condition on the singularity of g(z) at \(z=0\) and supposing that all constants \(\{\gamma_ i\}\) have the same sign existence and uniqueness of a solution is proved.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3928018
zbMATH Keywords: vortex flow
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: interacting n-particle system
MaRDI profile type: Publication
full work available at URL: pjaa.61.287
OpenAlex ID: W2065634514
cites work: On the vortex flow in bounded domains
cites work: Q3992729
cites work: Hydrodynamics in two dimensions and vortex theory
cites work: A stochastic differential equation arising from the vortex problem
DOI: 10.3792/PJAA.61.287
description: scientific article; zbMATH DE number 3928018