TY - JOUR

T1 - Asymptotic behavior of solutions to the compressible navier-stokes equation around a time-periodic parallel flow

AU - Brezina, Jan

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

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U2 - 10.1137/12089555X

DO - 10.1137/12089555X

M3 - Article

AN - SCOPUS:84892623330

VL - 45

SP - 3514

EP - 3574

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 6

ER -