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We consider the initial value problem for the Nernst--Planck equations coupled to the incompressible Euler equations in T². We prove global existence of weak solutions for vorticity in Lp with 2 ≤ p ≤ ∞. We also obtain global existence and uniqueness of smooth solutions. We show that smooth solutions of the Nernst--Planck--Navier--Stokes equations converge to solutions of the Nernst--Planck--Euler equations as viscosity tends to zero. All the results hold for large data. [ABSTRACT FROM AUTHOR]

We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (GSQG) equations. We derive a cubic approximation of the contour dynamics equation, and prove the short-time well-posedness of the approximate equations for generalized surface quasi-geostrophic fronts and weak well-posedness for surface quasi-geostrophic fronts. [ABSTRACT FROM AUTHOR]