Singularities of ElectroHydroDynamic Equations

• Applicant: Professor Dr. Georg Sebastian Weiss
• Subject Area: Mathematics
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 245812409

• Final Report Year: 2016

Final Report 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 the fluid region is asymptotically a cusp. Our proofs depend on a combination of monotonicity formulas and a non-vanishing result by Caffarelli-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.

Publications

• Singularities in Axisymmetric Free Boundaries for ElectroHydroDynamic Equations, Archive for Rational Mechanics and Analysis, November 2016, Volume 222, Issue 2, pp 573–601
  Garcia, Mariana Smit Vega and Vărvărucă, Eugen and Weiss, Georg S.
  (See online at https://doi.org/10.1007/s00205-016-1008-9)