On decay properties of the Stokes equations in exterior domains

1990 ◽  
pp. 134-151 ◽  
Author(s):  
Hermann Sohr ◽  
Werner Varnhorn
Keyword(s):  
Stokes Equations ◽  
Exterior Domains ◽  
Decay Properties

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

scholarly journals On the steady Navier–Stokes equations in 2D exterior domains

2020 ◽  
Vol 269 (3) ◽  
pp. 1796-1828 ◽  
Author(s):  
Mikhail V. Korobkov ◽  
Konstantin Pileckas ◽  
Remigio Russo
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Exterior Domains ◽  
Navier Stokes Equations
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