### Abstract

A new method for finding solutions of “Two-dimensional Navier-Stokes equations” (2D NSE) is discussed with using an adaptive fuzzy algorithm in this investigation, and the design target of this proposed method is to construct fuzzy solutions to satisfy the 2D NSE precisely and simultaneously. For achieving this design target, two rough fuzzy solutions are formulated as regressive forms with adjustable parameters firstly. Based on these two rough fuzzy solutions, an error cost function which is the square summation of approximation errors of boundary conditions, continuum equation and Navier- Stokes equations is minimized by a set of adaptive laws which can optimally tune the adjustable parameters of the proposed fuzzy solutions. Furthermore, approximated error bounds between the exact solutions and the proposed fuzzy solutions with respect to the number of fuzzy rules and solution errors have also been proven mathematically. Finally, the error equations in mesh points can be proven to converge to zero for the solution finding problem of 2D NSE.

Original language | English |
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Title of host publication | Handbook on Navier-Stokes Equations |

Subtitle of host publication | Theory and Applied Analysis |

Publisher | Nova Science Publishers, Inc. |

Pages | 209-228 |

Number of pages | 20 |

ISBN (Electronic) | 9781536103083 |

ISBN (Print) | 9781536102925 |

Publication status | Published - 2017 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Handbook on Navier-Stokes Equations: Theory and Applied Analysis*(pp. 209-228). Nova Science Publishers, Inc..

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*Handbook on Navier-Stokes Equations: Theory and Applied Analysis.*Nova Science Publishers, Inc., pp. 209-228.

**Fuzzy solutions of 2D navier-stokes equations.** / Chen, Yung-Yu.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Fuzzy solutions of 2D navier-stokes equations

AU - Chen, Yung-Yu

PY - 2017/1/1

Y1 - 2017/1/1

N2 - A new method for finding solutions of “Two-dimensional Navier-Stokes equations” (2D NSE) is discussed with using an adaptive fuzzy algorithm in this investigation, and the design target of this proposed method is to construct fuzzy solutions to satisfy the 2D NSE precisely and simultaneously. For achieving this design target, two rough fuzzy solutions are formulated as regressive forms with adjustable parameters firstly. Based on these two rough fuzzy solutions, an error cost function which is the square summation of approximation errors of boundary conditions, continuum equation and Navier- Stokes equations is minimized by a set of adaptive laws which can optimally tune the adjustable parameters of the proposed fuzzy solutions. Furthermore, approximated error bounds between the exact solutions and the proposed fuzzy solutions with respect to the number of fuzzy rules and solution errors have also been proven mathematically. Finally, the error equations in mesh points can be proven to converge to zero for the solution finding problem of 2D NSE.

AB - A new method for finding solutions of “Two-dimensional Navier-Stokes equations” (2D NSE) is discussed with using an adaptive fuzzy algorithm in this investigation, and the design target of this proposed method is to construct fuzzy solutions to satisfy the 2D NSE precisely and simultaneously. For achieving this design target, two rough fuzzy solutions are formulated as regressive forms with adjustable parameters firstly. Based on these two rough fuzzy solutions, an error cost function which is the square summation of approximation errors of boundary conditions, continuum equation and Navier- Stokes equations is minimized by a set of adaptive laws which can optimally tune the adjustable parameters of the proposed fuzzy solutions. Furthermore, approximated error bounds between the exact solutions and the proposed fuzzy solutions with respect to the number of fuzzy rules and solution errors have also been proven mathematically. Finally, the error equations in mesh points can be proven to converge to zero for the solution finding problem of 2D NSE.

UR - http://www.scopus.com/inward/record.url?scp=85030226989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030226989&partnerID=8YFLogxK

M3 - Chapter

SN - 9781536102925

SP - 209

EP - 228

BT - Handbook on Navier-Stokes Equations

PB - Nova Science Publishers, Inc.

ER -