 0721 Tepper L Gill and Woodford W Zachary
 GLOBAL (IN TIME) SOLUTIONS TO THE 3DNAVIERSTOKES
EQUATIONS ON R^3
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Jan 26, 07

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Abstract. A wellknown unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time solutions to the threedimensional NavierStokes equations. (These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces.) A related problem is to provide conditions under which we can be assured that the numerical approximation of these equations, used in a variety of fields from weather prediction to submarine design, have only one solution. In earlier papers, we solved this problem for a bounded domain. In this paper, we use an approach based on additional physical insight, that allows us to prove that there exists unique global in time solutions to the NavierStokes equations on R^3.
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