For more information about this meeting, contact Kris Jenssen.
| Title: | Global solutions to the homogeneous and inhomogeneous Navier-Stokes equations |
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| Seminar: | CCMA PDEs and Numerical Methods Seminar Series |
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| Speaker: | Tepper L. Gill, Howard University |
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| Abstract: |
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| In this talk, I discuss the construction of the largest separable Hilbert space SD2[R3], for
which the Leray-Hopf (weak) solutions on R3 are strong solutions in SD2 [R3 ] . In addition, we provide a new proof of global-in-time strong solutions, which leads to essentially the same proof for both bounded and unbounded domains and for a
homogeneous or inhomogeneous incompressible fluid. In particular, on SD2[R3] we are able to obtain strong a priori estimates for the nonlinear term. When the body forces are zero, we prove that there exists a positive constant u_+ , such that, for all divergence-free
vector fields in a dense set D contained in the closed ball B of radius 1/2 (1-\epsilon )u_+ , 0 < \epsilon < 1, the Navier-Stokes initial value problem has unique global strong
solutions in C1[(0,!), B]. When body forces are present, we obtain the same result for divergence-free vector fields in a dense set D contained in the annulus bounded by constants u_- and 1/2 u_+ . In either case (with or without body forces), we obtain
uniqueness for the Leray-Hopf (weak) solutions on R3 . Moreover, with mild conditions on the decay properties of the initial data, we obtain point-wise and time-decay of the solutions. However, our methods do not allow us to resolve the singularity question. If
time permits, I will discuss the relationship of SD2[R3] to other spaces used to study global solutions on R3 . |
Room Reservation Information
| Room Number: | MB216 |
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| Date: | 11 / 07 / 2011 |
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| Time: | 03:35pm - 04:25pm |
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