Global existence of strong solution for the Cucker-Smale-Navier-Stokes system

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We present a global existence theory for strong solution to the Cucker-Smale-Navier-Stokes system in a periodic domain, when initial data is sufficiently small. To model interactions between flocking particles and an incompressible viscous fluid, we couple the kinetic Cucker-Smale model and the incompressible Navier-Stokes system using a drag force mechanism that is responsible for the global flocking between particles and fluids. We also revisit the emergence of time-asymptotic flocking via new functionals measuring local variances of particles and fluid around their local averages and the distance between local averages velocities. We show that the particle and fluid velocities are asymptotically aligned to the common velocity, when the viscosity of the incompressible fluid is sufficiently large compared to the sup-norm of the particles' local mass density.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2014-09
Language
English
Article Type
Article
Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.257, no.6, pp.2225 - 2255

ISSN
0022-0396
DOI
10.1016/j.jde.2014.05.035
URI
http://hdl.handle.net/10203/278732
Appears in Collection
MA-Journal Papers(저널논문)
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