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...

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Bibliographic Details
Published in:Journal of mathematical fluid mechanics 2022-05, Vol.24 (2), Article 51
Main Authors: Abdo, Elie, Ignatova, Mihaela
Format: Article
Language:English
Subjects:
Boundary conditions
Classical and Continuum Physics
Exact solutions
Fluid flow
Fluid mechanics
Fluid- and Aerodynamics
Mathematical analysis
Mathematical Methods in Physics
Navier-Stokes equations
Norms
Physics
Physics and Astronomy
Species diffusion
Theoretical mathematics
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Summary: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.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-022-00665-8