Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows
Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows
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非等熵粒子流体流强解的全局适定性和最优大时间行为
DOI：
10.1007/s00526-020-01776-8
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Dehua Wang
中科院分区：
文献类型：
--
作者：
Yanmin Mu;Dehua Wang
本文研究了三维非等熵可压缩流固两相流动。该系统包括耦合之间的Vlasov-Fokker-Planck方程和非等熵可压缩Navier-Stokes方程通过动量和能量交换。对于给定平衡点附近的初始数据，我们证明了强解的全局适定性，并获得了三维全空间中的最佳代数收敛速度。对于周期域，当收敛速度为指数时，同样的全局适定性结果仍然成立。新的思想和技术的发展，以建立适定性和大时间的行为。对于整体适定性，我们的方法是基于新的宏-微分解，它对线性Fokker-Plank算子的谱依赖性较小，并具有精细的能量估计;而对于最优大时间行为的证明依赖于线性化Cauchy问题的Fourier分析和能量谱方法，其中我们提供了一些新的技术来处理非线性项.
In this paper, we study the three-dimensional non-isentropic compressible fluid–particle flows. The system involves coupling between the Vlasov–Fokker–Planck equation and the non-isentropic compressible Navier–Stokes equations through momentum and energy exchanges. For the initial data near the given equilibrium we prove the global well-posedness of strong solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. For the periodic domain the same global well-posedness result still holds while the convergence rate is exponential. New ideas and techniques are developed to establish the well-posedness and large-time behavior. For the global well-posedness our methods are based on the new macro–micro decomposition which involves less dependence on the spectrum of the linear Fokker–Plank operator and fine energy estimates; while the proofs of the optimal large-time behavior rely on the Fourier analysis of the linearized Cauchy problem and the energy-spectrum method, where we provide some new techniques to deal with the nonlinear terms.