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 -