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Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations

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 \({\mathbb{R} \times \mathbb{T}^2}\) . 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 x2 and x3 and its interactions with the planar rarefaction wave in x1 direction.

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Correspondence to Teng Wang.

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Communicated by L. Székelyhidi

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Li, La., Wang, T. & Wang, Y. Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations. Arch Rational Mech Anal 230, 911–937 (2018). https://doi.org/10.1007/s00205-018-1260-2

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