On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

2020 ◽  
Author(s):  
Tomoyuki Nakatsuka
Keyword(s):  
Periodic Solutions ◽  
Stokes Equation ◽  
Decay Rates ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Pointwise Decay

scholarly journals DECAY PROPERTIES OF SOLUTIONS TO THE LINEARIZED COMPRESSIBLE NAVIER–STOKES EQUATION AROUND TIME-PERIODIC PARALLEL FLOW

2012 ◽  
Vol 22 (07) ◽  
pp. 1250007 ◽  
Author(s):  
JAN BŘEZINA ◽  
YOSHIYUKI KAGEI
Keyword(s):  
Periodic Function ◽  
Stokes Equation ◽  
Parallel Flow ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Convective Term ◽  
Navier Stokes Equation ◽  
Decay Properties ◽  
Linearized Problem ◽  
Time Periodic

Decay estimates on solutions to the linearized compressible Navier–Stokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L2 norm as an (n - 1)-dimensional heat kernel. Furthermore, it is proved that the asymptotic leading part of solutions is given by solutions of an (n - 1)-dimensional linear heat equation with a convective term multiplied by time-periodic function.

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