GLOBAL SOLUTIONS OF THE NERNST-PLANCK-EULER EQUATIONS

We consider the initial value problem for the Nernst-Planck equations coupled to the incompressible Euler equations in T-2. We prove global existence of weak solutions for vorticity in L-p with 2 <= p <= infinity. 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.

Automated summary

The study demonstrates the global existence and uniqueness of solutions to the coupled Nernst-Planck and Euler equations on T-2, including for high-order moment norms, and shows convergence to solutions of another set of equations as viscosity tends to zero. This applies to large data scenarios.