Global strong solution for the compressible Poisson–Nernst–Planck–Navier–Stokes system in 1D

Cuiyu Wang; Cuiyu Wang

doi:10.3934/math.20261208

AIMS Mathematics

2026, Volume 11, Issue 9: 30484-30508. doi: 10.3934/math.20261208

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Global strong solution for the compressible Poisson–Nernst–Planck–Navier–Stokes system in 1D

Cuiyu Wang ^,

School of Mathematics & Center for Applied Mathematics of Guangxi (Guangxi University), Guangxi University, Nanning 530004, China

Received: 13 July 2026 Revised: 08 September 2026 Accepted: 15 September 2026 Published: 20 September 2026
MSC : 35Q30, 76N10

This paper investigates a multi-species Poisson–Nernst–Planck–Navier–Stokes (PNP-NS) system coupled with a self-consistent electrostatic potential. On a one-dimensional bounded domain, we establish the global existence and uniqueness of strong solutions that allow for vacuum in the initial fluid density. This work extends the two-ion global well-posedness results of Chen [S. Chen, J. Math. Anal. Appl. 554 (2026) 129943] to arbitrary multi-ion configurations with distinct valences and diffusion coefficients.
- Poisson-Nernst-Planck-Navier-Stokes global existence,
- multi-ion,
- a priori estimates
Citation: Cuiyu Wang. Global strong solution for the compressible Poisson–Nernst–Planck–Navier–Stokes system in 1D[J]. AIMS Mathematics, 2026, 11(9): 30484-30508. doi: 10.3934/math.20261208

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Abstract

This paper investigates a multi-species Poisson–Nernst–Planck–Navier–Stokes (PNP-NS) system coupled with a self-consistent electrostatic potential. On a one-dimensional bounded domain, we establish the global existence and uniqueness of strong solutions that allow for vacuum in the initial fluid density. This work extends the two-ion global well-posedness results of Chen [S. Chen, J. Math. Anal. Appl. 554 (2026) 129943] to arbitrary multi-ion configurations with distinct valences and diffusion coefficients.

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