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NAVIER-STOKES DYNAMICS ON A DIFFERENTIAL ONE-FORM(Kyoto Conference on the Navier-Stokes Equations and their Applications)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Story, Troy L. |
| Copyright Year | 2006 |
| Abstract | After transforming the Navier-Stokes dynamic equation into a differential oneform on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x and the conjugate bk to the position as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as ∣∣xk∣∣ → ∞, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the principal differential one-form with the vortex vector, the Lagrangian is obtained. |
| Starting Page | 365 |
| Ending Page | 382 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| Volume Number | 1 |
| Alternate Webpage(s) | http://library.msri.org/preprints/files/2003/2003-015/2003-015.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
