### Abstract

There is given an application of pseudo-analysis in the the- ory of uid mechanics. First, the monotonicity of the components of the velocity for the solutions of Euler equations is proven, which allows to obtain the pseudo-linear superposition principle for Euler equations. This principle is proven also for the Navier-Stokes equations but with respect to two dif- ferent pairs of pseudo-operations. It is shown that Stokes equations satisfy the pseudo-linear superposition principle with respect to a pair of pseudo- operations which are generated with the same function of one variable.

Original language | English |
---|---|

Pages (from-to) | 5-23 |

Number of pages | 19 |

Journal | Acta Polytechnica Hungarica |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Euler equations
- Fluid mechanics
- Navier-Stokes equations
- Pseudo-linear superposition principle
- Semiring
- Stokes equations

### ASJC Scopus subject areas

- General
- Engineering(all)

### Cite this

*Acta Polytechnica Hungarica*,

*9*(2), 5-23.

**Basic equations of uid dynamics treated by pseudo-analysis.** / Pap, E.; Vivona, Doretta.

Research output: Contribution to journal › Article

*Acta Polytechnica Hungarica*, vol. 9, no. 2, pp. 5-23.

}

TY - JOUR

T1 - Basic equations of uid dynamics treated by pseudo-analysis

AU - Pap, E.

AU - Vivona, Doretta

PY - 2012

Y1 - 2012

N2 - There is given an application of pseudo-analysis in the the- ory of uid mechanics. First, the monotonicity of the components of the velocity for the solutions of Euler equations is proven, which allows to obtain the pseudo-linear superposition principle for Euler equations. This principle is proven also for the Navier-Stokes equations but with respect to two dif- ferent pairs of pseudo-operations. It is shown that Stokes equations satisfy the pseudo-linear superposition principle with respect to a pair of pseudo- operations which are generated with the same function of one variable.

AB - There is given an application of pseudo-analysis in the the- ory of uid mechanics. First, the monotonicity of the components of the velocity for the solutions of Euler equations is proven, which allows to obtain the pseudo-linear superposition principle for Euler equations. This principle is proven also for the Navier-Stokes equations but with respect to two dif- ferent pairs of pseudo-operations. It is shown that Stokes equations satisfy the pseudo-linear superposition principle with respect to a pair of pseudo- operations which are generated with the same function of one variable.

KW - Euler equations

KW - Fluid mechanics

KW - Navier-Stokes equations

KW - Pseudo-linear superposition principle

KW - Semiring

KW - Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=84861413346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861413346&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 5

EP - 23

JO - Acta Polytechnica Hungarica

JF - Acta Polytechnica Hungarica

SN - 1785-8860

IS - 2

ER -