4.5 Article

GLOBAL SOLUTIONS OF THE NERNST-PLANCK-EULER EQUATIONS

Journal

SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 53, Issue 5, Pages 5507-5547

Publisher

SIAM PUBLICATIONS
DOI: 10.1137/21M1390864

Keywords

Nernst-Planck; Euler; inviscid limit

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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.
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.

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