 |
Universität Augsburg
|
|
|
Universität Augsburg
|
|
Professor Dr. Jan Bouwe van den Berg
Vrije Universiteit Amsterdam
spricht am
Donnerstag, 23. November 2017
um
15:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| In nonlinear analysis we often simulate dynamics on a computer, or calculate a numerical solution to a partial differential equation. This gives very detailed, stimulating information. However, it would be even better if we can be sure that what we see on the screen genuinely represents a solution of the problem. In particular, rigorous validation of the computations would allow such objects to be used as ingredients of theorems. As an example, we focus on a rigorous numerical method to prove existence of periodic orbits in the forced Navier-Stokes equations. In the vorticity formulation we use Fourier series in both space and time. We solve for the Fourier coefficients in a Banach algebra of geometrically decaying sequences. We apply a Newton-Kantorovich type argument in a suitable neighborhood of a numerically computed candidate (the radii polynomial approach). This leads to an existence result for two-dimensional periodic orbits in the Navier-Stokes equations with so-called ``four vortex forcing''. This is joint work with Maxime Breden, Jean-Philippe Lessard and Lennaert van Veen. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Dirk Blömker |