The dynamics of three dimensional Kelvin-Voigt-Brinkman- Forchheimer equations in bounded domains is considered in this work. The existence and uniqueness of strong solution to the system is obtained by exploiting the $ m $-accretive quantization of the linear and nonlinear operators. The long-term behavior of solutions of such systems is also examined in this work. We first establish the existence of an absorbing ball in appropriate spaces for the semigroup associated with the solutions of the 3D Kelvin-Voigt-Brinkman-Forchheimer equations. Then, we prove that the semigroup is asymptotically compact, which implies the existence of a global attractor for the system. Next, we show the differentiability of the semigroup with respect to the initial data and then establish that the global attractor has finite Hausdorff and fractal dimensions. Furthermore, we establish the existence of an exponential attractor and discuss about its fractal dimensions for the associated semigroup of such systems. Finally, we discuss about the inviscid limit of the 3D Kelvin-Voigt-Brinkman-Forchheimer equations to the 3D Navier-Stokes-Voigt system and then to the simplified Bardina model.

中文翻译：

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3D Kelvin-Voigt-Brinkman-Forchheimer方程的整体和指数吸引子

在这项工作中考虑了三维Kelvin-Voigt-Brinkman-Forchheimer方程在有界域中的动力学。通过利用线性和非线性算子的$ m $可累加量化，可以得到系统强解的存在性和唯一性。在这项工作中还检查了此类系统解决方案的长期行为。我们首先在与3D Kelvin-Voigt-Brinkman-Forchheimer方程解相关的半群的适当空间中建立吸收球的存在。然后，我们证明了半群是渐近紧凑的，这意味着该系统存在全局吸引子。接下来，我们显示半群相对于初始数据的可微性，然后确定整体吸引子具有有限的Hausdorff和分形维数。此外，我们建立了指数吸引子的存在，并讨论了这类系统的相关半群的分形维数。最后，我们讨论将3D Kelvin-Voigt-Brinkman-Forchheimer方程的无粘极限限制为3D Navier-Stokes-Voigt系统，然后是简化的Bardina模型。