Analysis of the Landau Solution
ISBN 9783656016373
40 Seiten, Taschenbuch/Paperback
CHF 22.05
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Bachelor Thesis from the year 2010 in the subject Mathematics - Analysis, grade: 1,0, Technical University of Darmstadt, language: English, abstract: In 1944 Lev D. Landau found a non-trivial solution to a stationary Navier-Stokes flow on R³, which was symmetric around some axis and fulfilled the condition, that the velocity decayed linearly
and the pressure quadratically in -x-, depending on a parameter -1 1. As it turns out, such a modified Landau solution is no longer
a solution to a Navier-Stokes system - clearly not in the classical, but as well neither in the weak nor very
weak sense. If d = ±1, the velocity will be unbounded on the half line x1 = x2 = 0, ±x3 0.
In this case, we have a bit more insight in the behaviour of the modified Landau solution, yet still no physically reasonable interpretation can be given in the whole space R³. In any case, one can consider modified Landau solutions to be solutions in certain subsets of R³, where they yield some interesting streamline plots, which are also provided in this thesis. Furthermore, we give an overview over known results concerning the Landau solution.
and the pressure quadratically in -x-, depending on a parameter -1 1. As it turns out, such a modified Landau solution is no longer
a solution to a Navier-Stokes system - clearly not in the classical, but as well neither in the weak nor very
weak sense. If d = ±1, the velocity will be unbounded on the half line x1 = x2 = 0, ±x3 0.
In this case, we have a bit more insight in the behaviour of the modified Landau solution, yet still no physically reasonable interpretation can be given in the whole space R³. In any case, one can consider modified Landau solutions to be solutions in certain subsets of R³, where they yield some interesting streamline plots, which are also provided in this thesis. Furthermore, we give an overview over known results concerning the Landau solution.