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A random‐walk interpretation of the incompressible navier‐stokes equations
Author(s) -
Peskin Charles S.
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380613
Subject(s) - random walk , mathematics , compressibility , navier–stokes equations , limit (mathematics) , interpretation (philosophy) , stochastic process , pressure correction method , mathematical analysis , statistical physics , mechanics , physics , statistics , computer science , programming language
We introduce a stochastic process that roughly corresponds to a random walk of a single molecule in an incompressible fluid, and we consider the force (per unit volume) exerted by such a “molecule” on the rest of the fluid. Averaging this force over an ensemble of such molecules and taking an appropriate limit, we obtain the Navier‐Stokes equations. The origin of time‐irreversibility in these equations is discussed in terms of the model.