On Some Electroconvection Models

• 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