Interior Electroneutrality in Nernst–Planck–Navier–Stokes Systems

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by Nernst–Planck–Navier–Stokes system. In asymptotically stable cases blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions concentrations, we prove that charge density $$\rho $$ converges time to zero interior domain, ( $$\epsilon \rightarrow 0$$ ). The order limits is important; take first long then length. Thus, our main new results these concern densities steady states, as . infinite behaviors follow corollaries previous works [5, 6]. For unstable regime Dirichlet bounds are also electroneutral conditions, which electroneutrality achieved at any fixed > , exponentially fast $$L^p$$ all $$1\leqq p < \infty hold two oppositely charged species with arbitrary diffusivities, bounded domains smooth boundaries.