In this paper, we study the 3D dissipative fluid–dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the Navier–Stokes/Poisson–Nernst–Planck system. We prove that if the partial derivatives of two velocity components \((\partial _1 u_{1}, \partial _2 u_{2})\) satisfy \(\begin{aligned} \ \ \ \ \ \int _{0}^{T} \frac{\big \Vert (\partial _1 u_{1}, \partial _2 u_{2})(\cdot , t) \big \Vert ^{\frac{8}{5-4\alpha }}_{\dot{B}_{\infty ,\infty }^{-\alpha }}}{1 + \ln \big (e + \big \Vert (\partial _1 u_{1}, \partial _2 u_{2})(\cdot , t) \big \Vert _{\dot{B}_{\infty , \infty }^{-\alpha }}\big )} \, dt< \infty \quad \text {for} \quad 0< \alpha < 1, \end{aligned}\) then the local solution can be smoothly extended past the time \(t = T\) . Particularly, a regularity criterion is further established for the critical case \(\alpha =0\) . These results represent further improvements of previous studies by Zhao et al. (2016; 2019; 2025) and Wu (2019). Moreover, we extend the results by Zhang (2008) and Dong et al. (2010; 2011) for the incompressible Navier–Stokes equations.
