Preprint C127/2011
Two Cauchy Problems Associated to the Brinkman Flow
Michel Molina Del Sol
Keywords: Brinkman Flow | Kato's Quasilinear Theory | Parabolic Regularization | Comparison Principle and Bore-Like initial condition
In this work we deal with two Cauchy problems associated to the Brinkman Flow, which models fluid viscosity in certain types of porous media. In the first of them, we study the local and global well-posedness in Sobolev Spaces H^{s}(R^{n}), s>n/2+1; using Kato's Theory for Quasilinear Equations and Parabolic Regularization. Moreover, we study the same problem with Bore-Like initial conditions, and we establish local solutions in H^{s}(R), s>3/2, and a L^{2}-global estimate of that solution.