Abstract
We construct stochastic partial differential equations for the vorticity distribution of a two-dimensional simple fluid. The drift part of these equations is approximately given by the Navier-Stokes Equation and the diffusion part depends on the correlation assumptions for the positions of the centers of the vortices.
This research was supported by a grant from ONR. “The physical part, i.e., Remark 1.1, has been written by J. Adin Mann, Jr. alone; the mathematical part, i.e., the rest of the paper without Remark 1.1 has been written by Peter Kotelenez alone.”
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Dawson, D.A.: Stochastic evolution equations and related measure processes. J. Multivariate Anal. 5, 1–52 (1975).
Dynkin, E.B.: Markov processes 1. Springer, Berlin-New York (1965).
Kotelenez, P.: Existence, uniqueness and smoothenss for a class of function valued stochastic partial differential equations (preprint #91-111 Department of Mathematics and Statistics, Case Western Reserve University).
Kotelenez, P.: Stochastic partial differential equations for particle densities and vortices. (Manuscript in preparation).
Marchioro, C., Pulvirenti, M.: Hydrodynamics in two dimensions and vortex theory. Comm. Math. Phys. 84, 483–503 (1982).
Vaillancourt, J.: On the existence of random McKean-Vlasov limits for triangular arrays of exchangeable diffusions. Stoch. Anal. Appl. (1988).
Walsh, J.B.: An introduction to stochastic partial differential equations. In P.L. Hennequin (ed.) Ecole d'Ete de Probabilites de Saint-Flour XIV-1984. LN in Mathematics 1180. Berlin-Heidelberg-New York, Springer 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 International Federation for Information Processing
About this paper
Cite this paper
Kotelenez, P., Mann, J.A. (1992). Random vortex models and stochastic partial differential equations. In: Rozovskii, B.L., Sowers, R.B. (eds) Stochastic Partial Differential Equations and Their Applications. Lecture Notes in Control and Information Sciences, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007329
Download citation
DOI: https://doi.org/10.1007/BFb0007329
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55292-5
Online ISBN: 978-3-540-47015-1
eBook Packages: Springer Book Archive