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Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review
M Bendahmane1, F Karami2, M Zagour3
1Institut de Mathématiques de Bordeaux, Université de Bordeaux, 33076 Bordeaux Cedex, France.
Abstract:
This paper presents a survey and critical analysis of the mathematical literature on modeling of dynamic populations living in a fluid medium. The present review paper is divided into two main parts: The first part deals with the multiscale derivation of deterministic and stochastic cross-diffusion systems governed by the incompressible Navier-Stokes equations. The derivation is obtained from the underlying description at the microscopic scale in kinetic theory models according to the micro-macro decomposition method. In the second part of this review, we are delighted to present a new variety of mathematical models describing different applications, namely, the pursuit-evasion dynamics, cancer invasion, and virus dynamics. Finally, critical analysis and future research perspectives are discussed.
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