Mathematical Sciences: Existence and Numerical Approximation of Viscous, Compressible Flows

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This research program is concerned with the solutions to the Navier-Stokes equations in fluid mechanics. It addresses the question of existence of solutions, the qualitative nature of these solutions, the relationship between these solutions and the solutions of the corres- ponding inviscid flow problems, and the computation of the finite difference approximations of the exact solutions. The results of this research project are expected to lead to a better understanding of physcial systems involving compressible viscous fluid flows and hence a better design for these systems.