Mathematical Sciences: Aspects of Fluid Flows

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9307497 Schonbek This project consists of two parts: a) a study of the large time behavior of solutions to equations of magnetohydrodynamics and multiphase flow, and an investigation of the influence of the nonlinear terms on the behavior of the solutions in the far field. More precisely it will be shown that the nonlinear terms in frequency space produce some mixing of the modes which introduce long waves that will slow down the decay; b) a study of an analogue to a fluid motion on the circle, its stability and long time behavior. The expectation is that the methods used here can be extended to the three dimensional sphere.%%% These projects analyze models of viscous fluid equations which incorporate nonlinear effects. Interest is focused in understanding the behavior of the fluids as time gets large and one goal is to demonstrate that the motion of such fluids take longer in slowing down than the motion of fluids which are purely dissipative. This study could lead to a better understanding of turbulence and may find applications in weather prediction. ***