Browse > Article
http://dx.doi.org/10.4134/JKMS.2012.49.6.1163

SPATIAL DECAY BOUNDS FOR A TEMPERATURE DEPENDENT STOKES FLOW  

Song, Jong-Chul (Department of Applied Mathematics Hanyang University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.6, 2012 , pp. 1163-1174 More about this Journal
Abstract
This paper examines a temperature dependent Stokes flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the author establishes exponential decay of solutions in energy norm with distance from the finite end of the cylinder.
Keywords
spatial decay bounds; differential inequality; a temperature dependent Stokes flow;
Citations & Related Records
연도 인용수 순위
  • Reference
1 C. O. Horgan and L. T.Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math. 35 (1978), no. 1, 97-116.   DOI   ScienceOn
2 O. A. Ladyzhenskaya and V. A. Solonnikov, Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations, Russ. Math. Surveys 28 (1973), 43-82.
3 C. Lin and L. E. Payne, Spatial decay bounds in time-dependent pipe flow of an incom- pressible viscous fluid, SIAM J. Appl. Math. 65 (2004), no. 2, 458-474.   DOI   ScienceOn
4 L. E. Payne, Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453-488.   DOI   ScienceOn
5 L. E. Payne, A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov, IMA J. Appl. Math. 72 (2007), no. 5, 563-569.   DOI   ScienceOn
6 L. E. Payne and J. C. Song, Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows, Z. Angew. Math. Phys. 51 (2000), no. 6, 867-880.   DOI
7 L. E. Payne and J. C. Song, Spatial decay in a double diffusive convection problem in Darcy flow, J. Math. Anal. Appl. 330 (2007), no. 2, 864-875.   DOI   ScienceOn
8 L. E. Payne and J. C. Song, Spatial decay bounds for double diffusive convection in Brinkman flow, J. Differential Equations 244 (2008), no. 2, 413-430.   DOI   ScienceOn
9 J. C. Song, Improved decay estimates in time-dependent Stokes flow, J. Math. Anal. Appl. 288 (2003), no. 2, 505-517.   DOI   ScienceOn
10 B. Straughan, Stability and Wave Motion in Porous Media, Springer, New York, 2008.
11 C. O. Horgan, Recent developments concerning Saint-Venant's principle: a second update, Appl. Mech. Rev. 49 (1996), 101-111.   DOI   ScienceOn
12 K. A. Ames, L. E. Payne, and P. W. Schaefer, Spatial decay estimates in time-dependent Stokes flow, SIAM J. Math. Anal. 24 (1993), no. 6, 1395-1413.   DOI   ScienceOn
13 I. Babuoska and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972), pp. 1-359. Academic Press, New York, 1972.
14 C. O. Horgan, Recent developments concerning Saint-Venant's principle: an update, Appl. Mech. Rev. 42 (1989), no. 11, 295-303.   DOI
15 C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant's principle, Adv. in Appl. Mech. 23 (1983), 179-69.   DOI