Analysis of the Landau Solution

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 c