Asymptotic behavior of solutions to the compressible navier-stokes equation around a time-periodic parallel flow

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Abstract

The global in time existence of strong solutions to the compressible Navier-Stokes equation around time-periodic parallel flows in Rn, n ≥ 2, is established under smallness conditions on Reynolds number, Mach number, and initial perturbations. Furthermore, it is proved for n = 2 that the asymptotic leading part of solutions is given by a solution of the one-dimensional viscous Burgers equation multiplied by the time-periodic function. In the case n ≥ 3 the asymptotic leading part of solutions is given by a solution of the n -1-dimensional heat equation with the convective term multiplied by the time-periodic function.

Original languageEnglish
Pages (from-to)3514-3574
Number of pages61
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number6
DOIs
Publication statusPublished - Dec 1 2013

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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