Reconstruction of the velocity from the vorticity in three-dimensional fluid flows

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 454, Issue 1970, 1998, Pages 607-630

  Auchmuty, Giles ^a  

^a University of Houston   (United States)

Author keywords

Boundary conditions; Harmonic vector fields; Potential representations; Variational principles; Velocity reconstruction; Vorticity

Indexed keywords

EID: 0040538319     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0176     Document Type: Article

References (15)

1. Amrouche, C., Bernardi, C., Dauge, M. & Girault, V. 1998 Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. (In the press.)
2. Auchmuty, G. 1994 Orthogonal decompositions and bases for three-dimensional vector fields. Num. Fund. Analyt. Opt. 15, 455-488.
3. Auchmuty, G. 1995 Potential representation of incompressible vector fields. Nonlinear Problems Appl. Math. SIAM 43-49.
4. Borchers, W. & Sohr, H. 1990 On the equations rot cccccccccv = g and div v = f with zero boundary conditions. Hokkaido Math. Jl 19, 67-87.
5. Bossavit, A. 1988 Magnetostatic problems in multiply connected regions: some properties of the curl operator. Proc. IEEA 135, 179-187.
6. Dautray, R. & Lions, J. L. 1990 Mathematical analysis and numerical methods for science and technology, vol. 3. Berlin: Springer.
7. Ferrari, A. B. 1993 On the blow-up of solutions of the 3-D Euler equations in a bounded domain. Commun. Math. Phys. 155, 277-294.
8. Foias, C. & Teman, R. 1978 Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation. Ann. Scuola Normale Superiors. Pisa V, 29-63.
9. Galdi, G. P. 1994 An introduction to the mathematical theory of the Navier-Stokes equations, vol. I. Berlin: Springer.
10. Girault, V. & Raviart, P. 1986 Finite element methods for the Navier-Stokes equations. Berlin: Springer.
11. Grisvard, P. 1985 Elliptic boundary value problems in nonsmooth domains. Boston, MA: Pitman.
12. Ladyzhenskaya, O. A. & Solonnikov, V. A. 1978 Some problems of vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations. J. Soviet Math. 19, 257-286.
13. Serrin, J. B. 1959 Mathematical principles of classical fluid mechanics. In Handbuch der Physik, Bd VIII/I, pp. 125-163. Berlin: Springer.
14. von Wahl, W. 1990 On necessary and sufficient conditions for the solvability of the equations rot u = γ and div u = ε with u vanishing on the boundary. In Springer Lecture Notes in Mathematics, vol. 1431, pp. 152-157. Berlin: Springer.
15. Zeidler, E. 1985 Nonlinear functional analysis and its applications, vol. III. Berlin: Springer.