Sufficiency Class for Global (in Time) Solutions to the ThreeDimensional NavierStokes Equations
Tepper L. Gill Howard University, Department of Electrical and Computer Engineering
Tuesday, February 6, 2007 15:0016:00, Building 101, Lecture Room D Gaithersburg Tuesday, February 6, 2007 13:0014:00, Room 4511 Boulder
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, has only one solution.
In this talk, I will discuss an approach, based on additional physical insight,
which allows us to prove that there exists a number u_{+} such that for all initial velocities in a ball
of radius u_{+}, the NavierStokes equations have unique global in time solutions
and the numerical approximation of these equations has only one solution.
Presentation Slides:
PDF (Slides),
PDF (Global (in Time) Solutions to the 3DNavierStokes Equations on R3),
PDF (Sufficiency Class for Global (in Time) Solutions to the 3DNavierStokes Equations),
PDF (Sufficiency Class for Global (in Time) Solutions to the 3DNavierStokes Equations in V)
Contact: F. HuntNote: Visitors from outside NIST must contact
Robin Bickel; (301) 9753668;
at least 24 hours in advance.
