### Abstract

The convergence from a sequence of the unique global solutions to the Cauchy problems for compressible viscoelastic fluids to a unique global solution of the incompressible Navier-Stokes equations without external forces is studied for a wide class of initial data as the Mach number and the elastic coefficient go to zero simultaneously. The proofs are based on a set of conservation laws and a list of estimates which are uniform in the scaling parameter as well as a dispersive estimate for the wave equation.

Original language | English (US) |
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Title of host publication | Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao |

Publisher | World Scientific Publishing Co. |

Pages | 243-269 |

Number of pages | 27 |

ISBN (Print) | 9789814578097, 9789814578073 |

DOIs | |

State | Published - Jan 1 2014 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)

### Cite this

*Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao*(pp. 243-269). World Scientific Publishing Co.. https://doi.org/10.1142/9789814578097_0016

**Scaling limit for compressible viscoelastic fluids.** / Hu, Xianpeng; Lin, Fang-Hua.

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

*Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao.*World Scientific Publishing Co., pp. 243-269. https://doi.org/10.1142/9789814578097_0016

}

TY - CHAP

T1 - Scaling limit for compressible viscoelastic fluids

AU - Hu, Xianpeng

AU - Lin, Fang-Hua

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The convergence from a sequence of the unique global solutions to the Cauchy problems for compressible viscoelastic fluids to a unique global solution of the incompressible Navier-Stokes equations without external forces is studied for a wide class of initial data as the Mach number and the elastic coefficient go to zero simultaneously. The proofs are based on a set of conservation laws and a list of estimates which are uniform in the scaling parameter as well as a dispersive estimate for the wave equation.

AB - The convergence from a sequence of the unique global solutions to the Cauchy problems for compressible viscoelastic fluids to a unique global solution of the incompressible Navier-Stokes equations without external forces is studied for a wide class of initial data as the Mach number and the elastic coefficient go to zero simultaneously. The proofs are based on a set of conservation laws and a list of estimates which are uniform in the scaling parameter as well as a dispersive estimate for the wave equation.

UR - http://www.scopus.com/inward/record.url?scp=84967373155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967373155&partnerID=8YFLogxK

U2 - 10.1142/9789814578097_0016

DO - 10.1142/9789814578097_0016

M3 - Chapter

AN - SCOPUS:84967373155

SN - 9789814578097

SN - 9789814578073

SP - 243

EP - 269

BT - Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao

PB - World Scientific Publishing Co.

ER -