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ON THE CAUCHY PROBLEM ASSOCIATED TO THE BRINKMAN FLOW IN R^nKeywords: Brinkman Equation , Cauchy Problem , Comparison Principle , Parabolic Regularization Abstract: In this work we deal with the Cauchy problem associated to the Brinkman flow, which models fluid flow in certain types of porous media. We study local and global well-posedness in Sobolev spaces $H^{s}(mathbb{R}^{n}), s>displaystylefrac{n}{2}+1,$ using Kato's theory for quasilinear equations and parabolic regu-larization.
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