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Global solutions to the Nernst-Planck-Euler system on bounded domain

Dapeng DuJingyu LiYansheng MaRuyi Pang
Dec 2022
摘要
We show that the Nernst-Planck-Euler system, which models ionicelectrodiffusion in fluids, has global strong solutions for arbitrarily largedata in the two dimensional bounded domains. The assumption on species iseither there are two species or the diffusivities and the absolute values ofionic valences are the same if the species are arbitrarily many. In particular,the boundary conditions for the ions are allowed to be inhomogeneous. The proofis based on the energy estimates, integration along the characteristic line andthe regularity theory of elliptic and parabolic equations.
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