Spatial Decay Estimates for the Navier–Stokes Equations with Application to the Problem of Entry Flow

Spatial Decay Bounds of Solutions to the Navier-Stokes Equations for Transient Compressible Viscous Flow

“…These pipe or channel flow results may be regarded as Saint-Venant type decay estimates. In fact, the first paper to point out this connection is that of Horgan and Wheeler [11]. For other results of Saint-Venant type, see [8], [13], [14], [22], [23].…”

“…Estimates of Saint-Venant type which exhibit exponential spatial decay in transient heat conduction problems appear to have originated with Boley, who shows the spatial decay of end effect at any time t in transient problems is faster than or at least equal to that the steady case [3]. Many authors have contributed to the literature on SaintVenant type estimates for parabolic and elliptic problems as well as for the more general Phragmén-Lindelöf type principles which result in an alternative of growth or decay (see [1], [2], [8], [10], [11], [12], [13], [14]). The survey article by Horgan and Knowles [9] and the updates by Horgan [6,7] discuss the history, rationale and the importance of such estimates and contain an extensive list of pertinent references.…”

“…( [1], [2], [8], [11], [13], [14], [24]). These pipe or channel flow results may be regarded as Saint-Venant type decay estimates.…”

Decay bounds for magnetohydrodynamic geophysical flow

“…We note that b and c involve E(0). It is shown in [7,10] that (3.7) is integrated to give To make (3.12) explicit we need a bound forÊ(0) or E(0) in terms of data, which we omit here. Theorem.…”

“…A number of spatial decay studies for problems involving various systems of differential equations have appeared in the literatures, e.g., for a survey of SaintVenant type spatial decay results see Hogran and Knowles [6] and Horgan [4,5], and for a decay estimates for the Navier-Stokes equations see Ames and Payne [1], and Horgan and Wheeler [7], and for other type spatial decay results see Quintailla [9] and Ames and Straughan [3]. More recently, Song [10] established exponential decay bounds for a problem in steady magnetohydrodynamical pipe flow.…”