Global large solutions to the Navier–Stokes–Nernst–Planck–Poisson equations in Fourier–Besov spaces

ABSTRACT

In this paper, we mainly study the Cauchy problem of a d-dimensional Navier–Stokes–Nernst–Planck–Poisson equation in Fourier–Besov space. Based on its special structure, the assumption of local smallness of the initial data can be ignored to obtain the global well-posedness, and it is proved that the global existence of the solution can be obtained only if part of the initial data is small enough.

KEYWORDS:

• Navier–Stokes–Nernst– Planck–Poisson equations
• large solutions
• Fourier–Besov spaces

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 42B37
• 35Q35
• 35K55
• 76B03

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by the NNSF of China [grant #11601223].