Long time dynamics of Nernst-Planck-Navier-Stokes systems

Article Mathematics, Applied

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

Elie Abdo et al.

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.

JOURNAL OF MATHEMATICAL FLUID MECHANICS (2022)

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Article Mathematics, Applied

Nernst-Planck-Navier-Stokes Systems far from Equilibrium

Peter Constantin et al.

Summary: The Nernst-Planck-Navier-Stokes system has global smooth solutions in bounded domains with smooth boundaries in three space dimensions. The solutions remain smooth for arbitrary positive Dirichlet boundary conditions for ionic concentrations, arbitrary Dirichlet boundary conditions for potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. Global regularity is maintained when considering multiple ionic species with the same diffusivities.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

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Article Mathematics

LONG TIME DYNAMICS OF A MODEL OF ELECTROCONVECTION

Elie Abdo et al.

Summary: The study investigates a model of electroconvection with a two dimensional viscous fluid carrying electrical charges and interacting with them. It shows that the system has a compact, finite dimensional global attractor in a mean zero frame associated with each solution. If the fluid is only forced by electrical forces, the attractor reduces to a single point.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

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Article Mathematics, Applied

Long time finite dimensionality in charged fluids

Elie Abdo et al.

Summary: The study focuses on the long time dynamics of solutions of 2D periodic Nernst-Planck-Navier-Stokes systems driven by body charges and body forces. It is demonstrated that in the absence of body charges but with fluid body forces present, the charge density of the ions exponentially converges to zero, and the ion concentrations exponentially converge to time independent constants. Meanwhile, the fluid remains dynamically active throughout the process. In the general case of body charges and body forces, the solutions converge in time to an invariant finite dimensional compact set in phase space.

NONLINEARITY (2021)

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Article Mathematics, Applied