Vanishing viscosity limit to rarefaction waves for the full compressible fluid models of Korteweg type

Wenjun Wang; Lei Yao

doi:10.3934/cpaa.2014.13.2331

Article Contents

2014, Volume 13, Issue 6: 2331-2350. Doi: 10.3934/cpaa.2014.13.2331

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Vanishing viscosity limit to rarefaction waves for the full compressible fluid models of Korteweg type

Wenjun Wang^1, and
Lei Yao^2,

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093
2.
School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127

Received: September 30, 2013

Revised: March 31, 2014

Published: October 2014

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Abstract

We prove the solution of the full compressible fluid models of Korteweg type with centered rarefaction wave data of large strength exists globally in time. As the viscosity, heat-conductivity and capillary coefficients tend to zero, the global solution converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly when the initial perturbation is small. Our analysis is based on the energy method.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35M10.

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References

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