Author
Carrillo de la Plata, J
Wroblewska-Kaminska, A
Zatorska, E
Journal title
Mathematical Models and Methods in Applied Sciences
DOI
10.1142/S0218202519500027
Issue
1
Volume
29
Last updated
2024-04-21T22:26:16.387+01:00
Page
31-63
Abstract
Hydrodynamic systems arising in swarming modeling include nonlocal forces in the form of attractive–repulsive potentials as well as pressure terms modeling strong local repulsion. We focus on the case where there is a balance between nonlocal attraction and local pressure in presence of confinement in the whole space. Under suitable assumptions on the potentials and the pressure functions, we show the global existence of weak solutions for the hydrodynamic model with viscosity and linear damping. By introducing linear damping in the system, we ensure the existence and uniqueness of stationary solutions with compactly supported density, fixed mass and center of mass. The associated velocity field is zero in the support of the density. Moreover, we show that global weak solutions converge for large times to the set of these stationary solutions in a suitable sense. In particular cases, we can identify the limiting density uniquely as the global minimizer of the free energy with the right mass and center of mass.
Symplectic ID
1098236
Favourite
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Publication type
Journal Article
Publication date
28 Dec 2018
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