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A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data

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    * Corresponding author 

The work of S.-Y. Ha is supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03, the work of Qinghua Xiao was supported by grants from Youth Innovation Promotion Association and the National Natural Science Foundation of China #11871469, #11501556, and the work of Xiongtao Zhang was supported by grant the National Natural Science Foundation of China #11801194

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  • We present a two-dimensional coupled system for flocking particle-compressible fluid interactions, and study its global solvability for the proposed coupled system. For particle and fluid dynamics, we employ the kinetic Cucker-Smale-Fokker-Planck (CS-FP) model for flocking particle part, and the isentropic compressible Navier-Stokes (N-S) equations for the fluid part, respectively, and these separate systems are coupled through the drag force. For the global solvability of the coupled system, we present a sufficient framework for the global existence of classical solutions with large initial data which can contain vacuum using the weighted energy method. We extend an earlier global solvability result [20] in the one-dimensional setting to the two-dimensional setting.

    Mathematics Subject Classification: Primary: 35A01, 35K45; Secondary: 76N10.


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