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The Cauchy problem of a fluid‐particle interaction model with external forces
Author(s) -
Jiang Zaihong,
Li Li,
Zhong Ning
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4606
Subject(s) - mathematics , uniqueness , cauchy problem , initial value problem , cauchy distribution , nonlinear system , mathematical analysis , uniqueness theorem for poisson's equation , physics , quantum mechanics
In this paper, we consider the Cauchy problem of a fluid‐particle interaction model with external forces. We first construct the asymptotic profile of the system. The global existence and uniqueness theorem for the solution near the profile is given. Finally, optimal decay rate of the solution to the background profile is obtained by combining the decay rate analysis of a linearized equation with energy estimates for the nonlinear terms. The main method used in this paper is the energy method combining with the macro‐micro decomposition.