Wed, 07.02.2018, 17:15 |
Do the Navier-Stokes equations correctly describe stationary fluid flows in two dimensions? Mathematisches Kolloquium Speaker: Prof. Dr. Peter Wittwer, Université de Genève Room: S2|14 /24 Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2/15), Schlossgartenstaße 7, statt.The construction of solutions to the stationary Navier-Stokes equations in R^{2} is a difficult mathematical problem, since the nonlinearity of the equations plays a dominant role. The corresponding linear problem, the Stokes equations, do not admit solutions of the expected type (Stokes paradox) and it was not clear until recently, if the Navier-Stokes equations do correctly describe stationary fluid flows in R^{2}. We give an introduction to the problem by presenting first detailed numerical and asymptotic results and by comparing with the three dimensional case which is well understood. Then, we discuss recent progress in the understanding of steady solutions to the Navier-Stokes equations in R^{2} and present results concerning the existence of weak solutions for the case of a source term with zero average. Finally, we discuss the difficulties that need to be overcome in order to obtain results for the case of a source term with nonzero average, for which new ideas will be needed in order to convert the rather detailed information which we have from asymptotic and numerical analysis into mathematical proofs. |
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Fachbereich Mathematik
Technische Universität Darmstadt
Schlossgartenstraße 7
64289 Darmstadt