Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Gradient flow structure for domain relaxation in Langmuir films

Authors: Mahir Hadžić and Govind Menon
Journal: Quart. Appl. Math. 70 (2012), 659-664
MSC (2000): Primary 76D07, 76A20, 35Q35
DOI: https://doi.org/10.1090/S0033-569X-2012-01263-7
Published electronically: June 22, 2012
MathSciNet review: 3052083
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We describe a gradient flow structure for the inviscid Langmuir layer Stokesian subfluid model introduced recently by Alexander et al. (2007).

References [Enhancements On Off] (What's this?)

  • 1. J. ALEXANDER, A. BERNOFF, E. MANN, J. MANN, J. WINTERSMITH, AND L. ZOU, Domain relaxation in Langmuir films, Journal of Fluid Mechanics, 571 (2007), pp. 191-219. MR 2293238 (2007m:76147)
  • 2. J. ALEXANDER, A. BERNOFF, E. MANN, J. MANN, AND L. ZOU, Hole dynamics in polymer Langmuir films, Physics of Fluids, 18 (2006), 10pp. MR 2243348
  • 3. R. ALMGREN, Singularity formation in Hele-Shaw bubbles, Physics of Fluids, 8 (1996), pp. 344-352. MR 1371519 (96j:76055)
  • 4. D.G. EBIN AND J. MARSDEN, Groups of diffeomorphisms and the motion of an incompressible fluid, Annals of Mathematics (2), 92 (1970), pp. 102-163. MR 0271984 (42:6865)
  • 5. D. LUBENSKY AND R. GOLDSTEIN, Hydrodynamics of monolayer domains at the air-water interface, Physics of Fluids, 8 (1996), pp. 843-854.
  • 6. F. OTTO, Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean-Field Theory, Archive for Rational Mechanics and Analysis, 141 (1998), pp. 63-103. MR 1613500 (2000j:76145)
  • 7. H. OMORI, On the group of diffeomorphisms on a compact manifold, Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., (1968) pp. 167-183, American Math. Society MR 0271983 (42:6864)
  • 8. L. SIMON, Lectures on geometric measure theory, Centre for Mathematical Analysis, Australian National University, 1984. MR 756417 (87a:49001)
  • 9. H. STONE AND H. MCCONNELL, Hydrodynamics of quantized shape transitions of lipid domains, Proceedings: Mathematical and Physical Sciences, 448 (1995), pp. 97-111.

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 76D07, 76A20, 35Q35

Retrieve articles in all journals with MSC (2000): 76D07, 76A20, 35Q35

Additional Information

Mahir Hadžić
Affiliation: Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139
Email: mahir.hadzic@math.uzh.ch

Govind Menon
Affiliation: Division of Applied Mathematics, Box F, Brown University, Providence, Rhode Island 02912
Email: menon@dam.brown.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01263-7
Received by editor(s): October 22, 2010
Published electronically: June 22, 2012
Additional Notes: The first author was supported by DMS 05-30862
The second author was supported by DMS 07-48482
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society