Diffusion on Viscous Fluids, Existence and Asymptotic Properties of Solutions

摘要

This document considers the motion of a mixture of two fluids, with a diffusion effect obeying Fick's law. The author considers the full non-linear problem and doesn't assume that lambda/micron is small. He proves the existence of a (unique) local solution, the existence of a global solution for small data, and the exponential decay to the equilibrium solution.