### 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 |

Subtitle of host publication | In Memory of Gu Chaohao |

Publisher | World Scientific Publishing Co. |

Pages | 243-269 |

Number of pages | 27 |

ISBN (Electronic) | 9789814578097 |

ISBN (Print) | 9789814578073 |

DOIs | |

State | Published - Jan 1 2014 |

### ASJC Scopus subject areas

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

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## Cite this

Hu, X., & Lin, F. (2014). Scaling limit for compressible viscoelastic fluids. In

*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