Sufficiency Class for Global (in Time) Solutions to the Three-Dimensional Navier-Stokes Equations
Tepper L. Gill
Howard University, Department of Electrical and Computer Engineering
Tuesday, February 6, 2007 15:00-16:00,
Building 101, Lecture Room D
Gaithersburg
Tuesday, February 6, 2007 13:00-14:00,
Room 4511
Boulder
Abstract:
A well-known 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 three-dimensional Navier-Stokes 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 Navier-Stokes 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 3D-Navier-Stokes Equations on R3),
PDF (Sufficiency Class for Global (in Time) Solutions to the 3D-Navier-Stokes Equations),
PDF (Sufficiency Class for Global (in Time) Solutions to the 3D-Navier-Stokes Equations in V)
Contact: F. HuntNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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