Scaling limit for compressible viscoelastic fluids

Xianpeng Hu, Fang-Hua Lin

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationFrontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao
PublisherWorld Scientific Publishing Co.
Pages243-269
Number of pages27
ISBN (Print)9789814578097, 9789814578073
DOIs
StatePublished - Jan 1 2014

Fingerprint

Viscoelastic Fluid
Scaling Limit
Compressible Fluid
Global Solution
Dispersive Estimates
scaling
Cauchy problem
fluids
Incompressible Navier-Stokes Equations
estimates
conservation laws
Mach number
lists
Navier-Stokes equation
Conservation Laws
wave equations
Wave equation
Cauchy Problem
Scaling
Zero

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

Hu, X., & Lin, F-H. (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

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

Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao. World Scientific Publishing Co., 2014. p. 243-269.

Research output: Chapter in Book/Report/Conference proceedingChapter

Hu, X & Lin, F-H 2014, Scaling limit for compressible viscoelastic fluids. in 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
Hu X, Lin F-H. Scaling limit for compressible viscoelastic fluids. In Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao. World Scientific Publishing Co. 2014. p. 243-269 https://doi.org/10.1142/9789814578097_0016
Hu, Xianpeng ; Lin, Fang-Hua. / Scaling limit for compressible viscoelastic fluids. Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao. World Scientific Publishing Co., 2014. pp. 243-269
@inbook{c830025be87c48a6911a997d43ba761a,
title = "Scaling limit for compressible viscoelastic fluids",
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.",
author = "Xianpeng Hu and Fang-Hua Lin",
year = "2014",
month = "1",
day = "1",
doi = "10.1142/9789814578097_0016",
language = "English (US)",
isbn = "9789814578097",
pages = "243--269",
booktitle = "Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics: In Memory of Gu Chaohao",
publisher = "World Scientific Publishing Co.",

}

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 -