Local existence and uniqueness of the dynamical equations of an incompressible membrane in two-dimensional space

Communications in Mathematical Sciences

Volumn 8, Issue 3, 2010, Pages 783-796

  Hu, Dan ^a   Song, Peng ^a   Zhang, Pingwen ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

And bending elasticity; Existence; Incompressible; Membrane; Uniqueness

Indexed keywords

EID: 77954642416     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2010.v8.n3.a9     Document Type: Article

References (20)

1. B. Alberts, etc. Essential Cell Biology, 2nd Edition, Garland Science/Taylor & Francis Group, 2003.
2. R. Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics, Courier Dover Publi-cations, 1990.
3. W. Cai and T. Lubensky, Hydrodynamics and dynamic fluctuations of fluid membranes, Phys. Rev. E, 4251, 1995.
4. H. Deuling and W. Helfrich, The curvature elasticity of fluid membranes: a catalogue of vesicle shapes, Journal de Physique. Tome, 37, 1335-1345, 1976.
5. Y. Fu, and R. Ogden, etc. Nonlinear Elasticity: Theory and Applications, Cambridge University Press, 2001.
6. J.H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics, Trafford Publishing, 2001.
7. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. Teil C, 28, 693-703, 1973.
8. T. Hou, J. Lowengrub and M. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys., 114, 312-338, 1994.
9. D. Hu, P. Zhang and W. E, Continuum theory of a moving membrane, Phys. Rev. E, 75, 4, 2007.
10. X. Li and Q. Nie, Surface diffusion on stressed solid surface, Commun. Comput. Phys., 2(1), 73-86, 2007.
11. M. Lomholt, P.L. Hansen and L. Miao, A general theory of non-equilibrium dynamics of lipid-protein fluid membranes, European Physical Journal E, 16, 439, 2005.
12. L. Miao, M. Lomholt and J. Kleis, Dynamics of shape fluctuations of quas-spherical vesicles revisited, European Physical Journal E, 9, 143, 2002.
13. Q. Nie, The nonlinear evolution of vortex sheets with surface tension in axi-symmetric flows, J. Comput. Phys., 174, 438-459, 2001.
14. C. Pozrikidis, Interfacial dynamics for Stokes flow, J. Comput. Phys., 169, 250-301, 2001.
15. L. Scriven, Dynamics of a fluid interface, Chem. Eng. Sci., 12-98, 1960.
16. U. Seifert, Fluid membranes in hydrodynamic flow fields: formalism and an application to fluctuating quasispherical vesicles in shear flow, European Physical Journal B, 8, 305, 1999.
17. P. Song, D. Hu and P. Zhang, Numerical simulation of fluid membranes in two-dimensional space, Commun. Comput. Phys., 3, 794-821, 2008.
18. D. Steigmann, Fluid films with curvature elasticity, Arch. Rat. Mech. Anal., 150, 127-152, 1999.
19. A. Waxman, Dynamics of a couple-stress fluid membrane, Studies in Applied Mathematics, 70, 63-86, 1984.
20. A. Waxman, A corotational time derivative for surface tensors, constitutive relations and a new measure of bending strain, J. Non-Newtonian Fluid Mech., 9-235, 1981.