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arXiv · 1203.1230

Zero dissipation limit of full compressible Navier-Stokes equations with Riemann initial data

Feimin Huang·Song Jiang·Yi Wang
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Abstract

We consider the zero dissipation limit of the full compressible Navier-Stokes equations with Riemann initial data in the case of superposition of two rarefaction waves and a contact discontinuity. It is proved that for any suitably small viscosity $\varepsilon$ and heat conductivity $\kappa$ satisfying the relation \eqref{viscosity}, there exists a unique global piecewise smooth solution to the compressible Navier-Stokes equations. Moreover, as the viscosity $\varepsilon$ tends to zero, the Navier-Stokes solution converges uniformly to the Riemann solution of superposition of two rarefaction waves and a contact discontinuity to the corresponding Euler equations with the same Riemann initial data away from the initial line $t=0$ and the contact discontinuity located at $x=0$.

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Feimin Huang, Song Jiang, Yi Wang. 2012-03-06. Zero dissipation limit of full compressible Navier-Stokes equations with Riemann initial data. https://arxiv.org/abs/1203.1230

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