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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Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 230; no. 3; pp. 911 - 937
Main Authors Li, Lin-an, Wang, Teng, Wang, Yi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2018
Springer Nature B.V
Subjects
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
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ISSN0003-9527
1432-0673
DOI10.1007/s00205-018-1260-2

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Summary: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.
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-018-1260-2