Stochastic Forcing in Hydrodynamic Models with Non-local Interactions

Pavel Ludvík () and Václav Mácha ()
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Pavel Ludvík: Palacký University Olomouc
Václav Mácha: Institute of Mathematics of the Czech Academy of Sciences

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2806-2852

Abstract: Abstract The hydrodynamical model of the collective behavior of animals consists of the Euler equation with additional non-local forcing terms representing the repulsive and attractive forces among individuals. This paper deals with the system endowed with an additional white-noise forcing and an artificial viscous term. We provide a proof of the existence of a dissipative martingale solution—a cornerstone for a subsequent analysis of the system with stochastic forcing.

Keywords: 35Q35; 35Q91 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01137-x

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