JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SPATIAL DECAY BOUNDS OF SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR TRANSIENT COMPRESSIBLE VISCOUS FLOW
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SPATIAL DECAY BOUNDS OF SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR TRANSIENT COMPRESSIBLE VISCOUS FLOW
Liu, Yan; Qiu, Hua; Lin, Changhao;
  PDF(new window)
 Abstract
In this paper, spatial decay estimates for the time dependent compressible viscous isentropic flow in a semi-infinite three dimensional pipe are derived. An upper bound for the total energy in terms of the initial boundary data is obtained as well. The results established in this paper may be viewed as a version of Saint-Venant's principle in transient compressible Navier-Stokes flow.
 Keywords
Navier-Stokes equations;transient compressible viscous flow;spatial decay estimate;Saint-Venant's principle;
 Language
English
 Cited by
 References
1.
K. A. Ames and L. E. Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal. 20 (1989), no. 4, 789-915. crossref(new window)

2.
K. A. Ames, L. E. Payne, and J. C. Song, Spatial decay in the pipe flow of a viscous fluid interfacing a porous medium, Math. Models Methods Appl. Sci. 11 (2001), no. 9, 1547-1562.

3.
B. A. Boley, Upper bounds and Saint-Venant's principle in transient heat conduction, Quart. Appl. Math. 18 (1960), 205-207.

4.
D. Hoff, Global solutions of the Navier-Stokes equations for multidimensional com-pressible flow with discontinuous initial data, J. Differential Equations 120 (1995), no. 1, 215-254. crossref(new window)

5.
D. Hoff, Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat conducting fluids, Arch. Ration Mech. Anal. 139 (1997), no. 4, 303-354. crossref(new window)

6.
C. O. Horgan, Recent development concerning Saint-Venant's principle: An update, Appl. Mech. Rev. 42 (1989), no. 11, part 1, 295-303. crossref(new window)

7.
C. O. Horgan, Recent development concerning Saint-Venant's principle: An second update, Appl. Mech. Rev. 49 (1996), 101-111. crossref(new window)

8.
C. O. Horgan, Plane entry flows and energy estimates for the Navier-Stokes equations, Arch. Ration Mech. Anal. 68 (1978), no. 4, 359-381.

9.
C. O. Horgan and J. K. Knowles, Recent development concerning Saint-Venant's prin-ciple, Adv. in Appl. Mech. 23 (1983), 179-269. crossref(new window)

10.
C. O. Horgan and L. E. Payne, Phragmen-Lindelof type results for harmonic functions with nonlinear boundary conditions, Arch. Ration Mech. Anal. 122 (1993), no. 2, 123-144. crossref(new window)

11.
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. crossref(new window)

12.
C. Lin and H. Li, A Phragmen-Lindelof alternative result for the Navier-Stokes equations for steady compressible viscous flow, J. Math. Anal. Appl. 340 (2008), no. 2, 1480-1492. crossref(new window)

13.
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 (2005), no. 2, 458-474.

14.
C. Lin and L. E. Payne, Spatial decay bounds in the channel flow of an incompressible viscous fluid, Math. Models Methods Appl. Sci. 14 (2004), no. 6, 795-818. crossref(new window)

15.
C. Lin and L. E. Payne, Phragmen-Lindelof type results for second order quasilinear parabolic equations in $R^{2}$, Z. Angew. Math. Phys. 45 (1994), no. 2, 294-311. crossref(new window)

16.
P. L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 2. Compressible Models, Oxford Lecture Series in Mathematics and its Applications, 10. Oxford Science Publi-cations. The Clarendon Press, Oxford University Press, New York, 1998.

17.
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of mo-tion of compressible viscous and heat-conductive fluids, Comm. Math. Phys. 89 (1983), no. 4, 445-464. crossref(new window)

18.
A. Matsumura and M. Padula, Stability of stationary flow of compressible fluid subject to large external potential force, SAACM 2 (1992), 183-202.

19.
A. Matsumura and N. Yamagata, Global weak solutions of the Navier-Stokes equations for multidimensional compressible flow subject to large external potential forces, Osaka J. Math. 38 (2001), no. 2, 399-418.

20.
L. E. Payne, Uniqueness criteria for steady state solutions of the Navier-Stokes equa-tions, Simpos. Internaz. Appl. Anal. Fis. Mat. (Cagliari-Sassari, 1964) pp. 130-153 Edi-zioni Cremonese, Rome, 1965.

21.
J. Serrin, The initial value problem for the Navier-Stokes equations, Nonlinear Problems (Proc. Sympos., Madison, Wis.) pp. 69-98 Univ. of Wisconsin Press, Madison, Wis., 1963.

22.
J. C. Song, Decay estimates in steady semi-inflnite thermal pipe flow, J. Math. Anal. Appl. 207 (1997), no. 1, 45-60. crossref(new window)

23.
J. C. Song, Spatial decay estimates in time-dependent double-diffusive Darcy plane flow, J. Math. Anal. Appl. 267 (2002), no. 1, 76-88. crossref(new window)

24.
J. C. Song, Improved decay estimates in time-dependent Stokes flow, J. Math. Anal. Appl. 288 (2003), no. 2, 505-517. crossref(new window)

25.
V. A. Vaigant and A. V. Kazhikhov, On the existence of global solutions of two- dimensional Navier-Stokes equations of a compressible viscous fluid, Sibirsk. Mat. Zh. 36 (1995), no. 6, 1283-1316;translation in Siberian Math. J. 36 (1995), no. 6, 1108-1141.