Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations
We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain R × T 2 . Compared with one-dimensional case, the proof here is based on our new observations...
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| Published in | Archive for rational mechanics and analysis Vol. 230; no. 3; pp. 911 - 937 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2018
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0003-9527 1432-0673 |
| DOI | 10.1007/s00205-018-1260-2 |
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| Abstract | We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain
R
×
T
2
. Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions
x
2
and
x
3
and its interactions with the planar rarefaction wave in
x
1
direction. |
|---|---|
| AbstractList | We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain
R
×
T
2
. Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions
x
2
and
x
3
and its interactions with the planar rarefaction wave in
x
1
direction. We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain R×T2 . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x2 and x3 and its interactions with the planar rarefaction wave in x1 direction. |
| Author | Wang, Yi Li, Lin-an Wang, Teng |
| Author_xml | – sequence: 1 givenname: Lin-an surname: Li fullname: Li, Lin-an organization: Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, School of Mathematical Sciences, University of Chinese Academy of Sciences – sequence: 2 givenname: Teng orcidid: 0000-0001-8624-5567 surname: Wang fullname: Wang, Teng email: tengwang@amss.ac.cn organization: College of Applied Sciences, Beijing University of Technology – sequence: 3 givenname: Yi surname: Wang fullname: Wang, Yi organization: School of Mathematical Sciences, University of Chinese Academy of Sciences, CEMS, HCMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences |
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Anal.201547324162425335762910.1137/1409998271325.35148 Klingenberg, C., Markfelder, S.: The Riemann problem for the multi-dimensional isentropic system of gas dynamicsis ill-posed if it contains a shock, to appear in Arch Rational Mech Anal 2017. https://doi.org/10.1007/s00205-017-1179-z NishikawaMNishiharaKAsymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensionsTrans. Amer. Math. Soc.2000352312031215149187210.1090/S0002-9947-99-02290-40933.35130 HuangFMXinZPYangTContact discontinuities with general perturbation for gas motionAdv. Math.200821912461297245061010.1016/j.aim.2008.06.0141155.35068 De LellisCSzékelyhidiLJrThe Euler equations as a differential inclusionAnn. of Math.2009170314171436260087710.4007/annals.2009.170.14171350.35146 ZumbrunKSerreDViscous and Inviscid Stability of Multidimensional Planar Shock FrontsIndiana U. Math. 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Anal.1986953253441986ArRMA..95..325G85378210.1007/BF002768400631.35058 MatsumuraANishiharaKOn the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gasJapan J. Appl. Math.19852172583931710.1007/BF031670360602.76080 HuangFMLiJ.MatsumuraA.Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier–Stokes systemArch. Rational Mech. Anal2010197891162010ArRMA.197...89H264681510.1007/s00205-009-0267-01273.76259 MJ Li (1260_CR20) 2015; 13 1260_CR4 J Goodman (1260_CR8) 1986; 95 TP Liu (1260_CR24) 2010; 5 TP Liu (1260_CR21) 1985; 56 K Nishihara (1260_CR30) 2004; 35 E Chiodaroli (1260_CR3) 2015; 68 1260_CR36 K. Ito (1260_CR15) 1996; 6 1260_CR34 FM Huang (1260_CR10) 2010; 197 QS Jiu (1260_CR16) 2013; 45 J Nash (1260_CR29) 1962; 90 1260_CR19 J Smoller (1260_CR32) 1994 K Zumbrun (1260_CR37) 1999; 48 1260_CR17 TP Liu (1260_CR22) 1988; 118 FM Huang (1260_CR11) 2009; 289 A Matsumura (1260_CR27) 1986; 3 FM Huang (1260_CR14) 2008; 219 A Matsumura (1260_CR28) 1992; 144 A Szepessy (1260_CR33) 1993; 122 A Matsumura (1260_CR26) 1985; 2 M Nishikawa (1260_CR31) 2000; 352 FM Huang (1260_CR13) 2016; 65 P Lax (1260_CR18) 1957; 10 ZP Xin (1260_CR35) 1990; 319 GQ Chen (1260_CR2) 2007; 4 1260_CR25 H Hokari (1260_CR9) 1997; 15 E Feireisl (1260_CR7) 2015; 47 FM Huang (1260_CR12) 2006; 179 1260_CR1 E Feireisl (1260_CR6) 2015; 12 C Lellis De (1260_CR5) 2009; 170 TP Liu (1260_CR23) 1997; 1 |
| References_xml | – reference: GoodmanJNonlinear asymptotic stability of viscous shock profiles for conservation lawsArch. Rational. Mech. Anal.1986953253441986ArRMA..95..325G85378210.1007/BF002768400631.35058 – reference: LiuTPYuSHViscous rarefaction wavesBull. Inst. Math. Acad. Sin. (N.S.)20105212317926814051216.35120 – reference: MatsumuraANishiharaKOn the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gasJapan J. Appl. Math.19852172583931710.1007/BF031670360602.76080 – reference: SzepessyAXinZPNonlinear stability of viscous shock wavesArch. Rational Mech. Anal.1993122531031993ArRMA.122...53S120724110.1007/BF018165550803.35097 – reference: Solonnikov, V. A.: On solvability of an initial-boundary value problem for the equations of motion of a viscous compressible fluid. In: Studies on Linear Operators and Function Theory. 6 [in Russain], Nauka, Leningrad, 128–142, 1976 – reference: Chiodaroli, E., Kreml, O.: Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations, preprint, arXiv:1704.01747. – reference: LiuTPXinZPNonlinear stability of rarefaction waves for compressible Navier-Stokes equationsComm. Math. Phys.19881184514651988CMaPh.118..451L95880610.1007/BF014667260682.35087 – reference: LiuTPNonlinear stability of shock waves for viscous conservation lawsMem. Amer. Math. Soc.1985561108791863 – reference: Klingenberg, C., Markfelder, S.: The Riemann problem for the multi-dimensional isentropic system of gas dynamicsis ill-posed if it contains a shock, to appear in Arch Rational Mech Anal 2017. https://doi.org/10.1007/s00205-017-1179-z – reference: MatsumuraANishiharaKAsymptotics toward the rarefaction wave of the solutions of a one-dimensional model system for compressible viscous gasJapan J. Appl. Math.1986311389921010.1007/BF031670880612.76086 – reference: FeireislEKremlOVasseurAStability of the isentropic Riemann solutions of the full multi-dimensional Euler systemSIAM J. Math. Anal.201547324162425335762910.1137/1409998271325.35148 – reference: LiuTPXinZPPointwise decay to contact discontinuities for systems of viscous conservation lawsAsian J. Math.199713484148099010.4310/AJM.1997.v1.n1.a30928.35095 – reference: HuangFMMatsumuraAXinZPStability of contact discontinuities for the 1-D compressible Navier–Stokes equationsArch. Rational Mech. Anal.200617955772006ArRMA.179...55H220828910.1007/s00205-005-0380-71079.76032 – reference: JiuQSWangYXinZPVacuum behaviors around rarefaction waves to 1D compressible Navier–Stokes equations with density-dependent viscositySIAM J. Math. Anal.20134531943228311664510.1137/1208799191293.35170 – reference: Li, L. 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| SubjectTerms | Classical Mechanics Complex Systems Compressibility Dimensional stability Fluid dynamics Fluid flow Fluid- and Aerodynamics Mathematical analysis Mathematical and Computational Physics Navier-Stokes equations Nozzles Physics Physics and Astronomy Rarefaction Theoretical Wave propagation |
| Title | Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations |
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