Skip to main content
SpringerLink
Log in

On Some Electroconvection Models

  • Published:
Journal of Nonlinear Science Aims and scope Submit manuscript

Abstract

We consider a model of electroconvection motivated by studies of the motion of a two-dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two electrodes. We prove that this electroconvection model has global in time unique smooth solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Cabre, X., Tan, J.: Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224(5), 2052–2093 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Constantin, P., Foias, C.: Navier–Stokes Equations. University of Chicago Press, Chicago (1988)

    MATH  Google Scholar 

  • Constantin, P., Ignatova, M.: Remarks on the Fractional Laplacian with Dirichlet Boundary Conditions and Applications. arXiv:1511.00147 (math.AP) (2015)

  • Constantin, P., Tarfulea, A., Vicol, V.: Long time dynamics of forced critical SQG. Commun. Math. Phys. 335, 93–141 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Constantin, P., Vicol, V.: Nonlinear maximum principles for dissipative linear nonlocal operators and applications. Geom. Funct. Anal. 22, 1289–1321 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Córdoba, A., Córdoba, D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys. 249, 511–528 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Daya, Z.A., Deyirmenjian, V.B., Morris, S.W., de Bruyn, J.R.: Annular electroconvection with shear. Phys. Rev. Lett. 80, 964–967 (1998)

    Article  Google Scholar 

  • Jerison, D., Kenig, C.: The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130, 161–212 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Lions, J.L.: Quelques Méthodes de Résolution des Problèmes Aux Limites non Linéaires. Dunod, Paris (1969)

    MATH  Google Scholar 

  • Resnick, S.G.: Dynamical problems in non-linear advective partial differential equations. Ph.D. Thesis, The University of Chicago. ProQuest LLC, Ann Arbor, MI (1995)

  • Tsai, P., Daya, Z.A., Deyirmenjian, V.B., Morris, S.W.: Direct numerical simulation of supercritical annular electroconvection. Phys. Rev. E 76, 1–11 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

The work of PC was partially supported by NSF Grant DMS-1209394. The work of VV was partially supported by NSF Grant DMS-1514771 and by an Alfred P. Sloan Research Fellowship.

Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Peter Constantin, Tarek Elgindi, Mihaela Ignatova & Vlad Vicol

Authors
  1. Peter Constantin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tarek Elgindi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mihaela Ignatova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vlad Vicol
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Constantin.

Additional information

Communicated by Edriss S. Titi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Constantin, P., Elgindi, T., Ignatova, M. et al. On Some Electroconvection Models. J Nonlinear Sci 27, 197–211 (2017). https://doi.org/10.1007/s00332-016-9329-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00332-016-9329-2

Keywords

Search

Navigation