Slightly compressible Brinkman–Forchheimer equations in a bounded 3D domain with Dirichlet boundary conditions are considered. These equations model fluids motion in porous media. The dissipativity of these equations in higher order energy spaces is obtained and regularity and smoothing properties of the solutions are studied. In addition, the existence of a global and an exponential attractors for these equations in a natural phase space is verified.

中文翻译：

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可压缩Brinkman–Forchheimer方程的渐近正则性和吸引子

考虑带Dirichlet边界条件的有界3D域中的可压缩Brinkman-Forchheimer方程。这些方程式模拟了多孔介质中的流体运动。获得了这些方程在高阶能量空间中的耗散性，并研究了解的正则性和平滑性。另外，验证了自然相空间中这些方程的整体吸引子和指数吸引子的存在。