#### Filter Results:

#### Publication Year

1998

2017

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- Alexander Rauh
- 2001

There is renewed interest in the question of whether the Navier–Stokes equations (NSE), one of the fundamental models of classical physics and widely used in engineering applications, are actually self-consistent. After recalling the essential physical assumptions inherent in the NSE, the notion of weak solutions, possible implications for the energy… (More)

A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of… (More)

- Alexander Rauh
- 2001

A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipa-tive dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds compact domains in phase space which contain the ω sets of all tra-jectories, in particular the fixed points, limit cycles,… (More)

The author wishes to make the following corrections to the published paper [1]: 1. Equation (35) is replaced with:

In the subcritical interval of the Reynolds number 4320 ≤ R ≤ R c ≡ 5772, the Navier–Stokes equations of the two–dimensional plane Poiseuille flow are approximated by a 22–dimensional Galerkin representation formed from eigenfunctions of the Orr–Sommerfeld equation. The resulting dynamical system is brought into a generalized normal form which is… (More)

- Alexander Rauh
- 2001

A comparative discussion of the normal form and action angle variable method is presented in a tuto-rial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on establishing a third integral of motion for the transformed Hamil-tonian truncated at finite order of the perturbation… (More)

- ‹
- 1
- ›