广义 Brinkman-Forchheimer 方程的渐近性态

Abstract

Abstract:

This article investigated the well-posedness and long-term behavior problems of solutions to 3D compressible generalized Brinkman-Forchheimer equation defined on a bounded domain. The equation simulates the transport process of fluid through porous medium dominated by Lévy dissipation. Firstly, the classical compactness method and a prior estimation were used to prove the well posedness of the solution of the equation in the energy space. Secondly, introduce the concept of system decomposition: on the one hand, the localization method was used to prove the boundedness of the contraction part of the equation in the initial energy space; on the other hand, the exponential dissipation of the smooth part of the equation in the high-order energy space is obtained by the instantaneous optical smoothing method, and the existence of the global attractor and the exponential attractor of the equation in the initial phase space is finally verified.

Key words: slightly compressible Brinkman-Forchheimer equation, well-posedness, regularity and partial smoothing, global attractor, exponential attractor.

CLC Number:

O175.2

Li Xin, Hao Wenjuan, Liu Yang. The Asymptotic Behavior of the Generalized Brinkman-Forchheimer Equation[J].Acta mathematica scientia,Series A, 2025, 45(1): 74-91.

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The Asymptotic Behavior of the Generalized Brinkman-Forchheimer Equation

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