Spatial Decay Estimates in Time-Dependent Stokes Flow

Spatial Decay Estimates in Time-Dependent Double-Diffusive Darcy Plane Flow

“…At the finite end of the channel, time-dependent data are prescribed, and homogeneous data are assumed on the top and bottom of the channel. We derive an explicit inequality which implies exponential decay of a weighted energy integral as a function of the distance from the finite end of the channel for each t. Decay results in steady double-diffusive convective Darcy and Brinkman flows have been studied by Payne and Song [12], who were able to eliminate the pressure term using the method developed by Horgan and Wheeler [7] and Ames et al [1]. In our time-dependent doublediffusive two-dimensional flow, we introduce a stream function to deal with the pressure term for establishing the decay estimate.…”

Spatial Decay Bounds for a Temperature Dependent Stokes Flow

“…With prescribed data on the finite end of the cylinder together with appropriate homogeneous initial conditions and boundary conditions on the lateral surface, Saint-Venant type decay results are established. Other decay results for Darcy flow, Stokes and Navier-Stokes flow have been obtained by Payne and Song [12], Ames et al [1], Song [14], Lin and Payne [8], and Horgan and Wheeler [6]. See for instance the survey papers of Horgan and Knowles [5], Horgan [3,4] and the book of Straughan [15].…”

Improved spatial decay bounds in generalized heat conduction

“…Saint-Venant type decay bounds for time dependent channel and pipe flow of viscous fluid may be found in [2,10,12,13,14,21]. Results in other time dependent problems are recorded in [5][6][7].…”

“…Various properties of solutions of this system have been investigated in the literature (see e.g. [2,[8][9][10][12][13][14][15]). In this paper we revisit the works of the authors [17,20] in which bounds for the decay of energy in a semi-infinite cylinder were obtained.…”