On the Space Analyticity of the Nernst-Planck-Navier-Stokes system

We consider the forced Nernst-Planck-Navier-Stokes system for n ionic species with different diffusivities and valences. We prove the local existence of analytic solutions with periodic boundary conditions in two and three dimensions. In the case of two spatial dimensions, the local solution extends uniquely and remains analytic on any time interval [0, T]. In the three dimensional case, we give necessary and sufficient conditions for the global in time existence of analytic solutions. These conditions involve quantitatively only low regularity norms of the fluid velocity and concentrations.

Automated summary

The forced Nernst-Planck-Navier-Stokes system for n ionic species with different diffusivities and valences is considered. The local existence of analytic solutions with periodic boundary conditions in two and three dimensions is proven. In the case of two spatial dimensions, the local solution extends uniquely and remains analytic on any time interval [0, T]. In the three dimensional case, necessary and sufficient conditions for the global in time existence of analytic solutions are given, which involve quantitatively only low regularity norms of the fluid velocity and concentrations.