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| Zero Dissipation Limit to Rarefaction Waves for the 1-D Compressible Navier-Stokes Equations |
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Citation： |
Feimin HUANG,Xing LI.Zero Dissipation Limit to Rarefaction Waves for the 1-D Compressible Navier-Stokes Equations[J].Chinese Annals of Mathematics B,2012,33(3):385~394 |
| Page view： 2256
Net amount： 1319 |
Authors： |
Feimin HUANG; Xing LI; |
Foundation： |
the National Natural Science Foundation of China for Outstanding Young Scholars (No.\,10825102) and the National Basic Research Program of China (973 Program) (No.\,2011CB808002). |
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| Abstract： |
The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible, isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper. In a paper (Comm. Pure Appl. Math., 46, 1993, 621--665) by Z. P. Xin, the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore, he obtained that the convergence rate is $\varepsilon^{\frac{1}{4}}|\ln\varepsilon|$. In this paper, Xin's convergence rate is improved to $\varepsilon^{\frac{1}{3}}|\ln\varepsilon|^2$ by different scaling arguments. The new scaling has various applications in related problems. |
Keywords： |
Compressible Navier-Stokes equations, Rarefaction wave, Compressible Euler equations |
Classification： |
17B40, 17B50 |
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