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On the space analyticity of the Nernst-Planck-Navier-Stokes system. (English) Zbl 1487.35310

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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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