A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data
A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data
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DOI：
10.3934/cpaa.2020039
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发表时间：
2020
影响因子：
1
通讯作者：
Seung‐Yeal Ha;Bingkang Huang;Qinghua Xiao;Xiongtao Zhang
中科院分区：
文献类型：
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作者：
Seung‐Yeal Ha;Bingkang Huang;Qinghua Xiao;Xiongtao Zhang
我们提出了一种用于植绒颗粒-可压缩流体相互作用的二维耦合系统，并研究了该耦合系统的全局可解性。对于粒子和流体动力学，我们分别对植绒粒子部分采用动力学 Cucker-Smale-Fokker-Planck (CS-FP) 模型，对流体部分采用等熵可压缩纳维斯托克斯 (N-S) 方程，并且这些单独的系统通过阻力耦合。对于耦合系统的全局可解性，我们提出了一个充分的框架，用于使用加权能量方法包含大量初始数据的经典解的全局存在性，这些初始数据可以包含真空。我们将一维设置中的早期全局可解性结果[20]扩展到二维设置。
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.