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Selected Works of Mariana Smit Vega Garcia
Article
Singularities in Axisymmetric Free Boundaries for ElectroHydroDynamic Equations
Archive for Rational Mechanics and Analysis (2016)
  • Mariana Smit Vega Garcia, University of Duisburg-Essen
  • Eugen Vărvărucă, “Al. I. Cuza” University
  • Georg S. Weiss, University of Duisburg-Essen
Link
Abstract
We consider singularities in the ElectroHydroDynamic equations. In a regime where we are allowed to neglect surface tension, and assuming that the free surface is given by an injective curve and that either the fluid velocity or the electric field satisfies a certain non-degeneracy condition, we prove that either the fluid region or the gas region is asymptotically a cusp. Our proofs depend on a combination of monotonicity formulas and a non-vanishing result by Caffarelli and Friedman. As a by-product of our analysis we also obtain a special solution with convex conical air-phase which we believe to be new.
Keywords
  • Free boundaries,
  • ElectroHydroDynamic equations
Disciplines
Publication Date
November, 2016
DOI
10.1007/s00205-016-1008-9
Citation Information
Mariana Smit Vega Garcia, Eugen Vărvărucă and Georg S. Weiss. "Singularities in Axisymmetric Free Boundaries for ElectroHydroDynamic Equations" Archive for Rational Mechanics and Analysis Vol. 222 Iss. 2 (2016) p. 573 - 601
Available at: http://works.bepress.com/mariana-smitvegagarcia/3/