Blow-up criteria for the three dimensional nonlinear dissipative system modeling electro-hydrodynamics. (October 2016)

• Record Type: Journal Article
• Authors: Zhao, Jihong; Bai, Meng
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 210
• Page End: 226
• Publication Date: 2016-10
• Subjects: Nonlinear dissipative system -- Electro-hydrodynamics -- Navier–Stokes equations -- Poisson–Nernst–Planck equations -- Blow-up criteria; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.016
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate some sufficient conditions for the breakdown of local smooth solutions to the three dimensional nonlinear nonlocal dissipative system modeling electro-hydrodynamics. This model is a strongly coupled system by the well-known incompressible Navier–Stokes equations and the classical Poisson–Nernst–Planck equations. We show that the maximum of the vorticity field alone controls the breakdown of smooth solutions, which reveals that the velocity field plays a more dominant role than the density functions of charged particles in the blow-up theory of the system. Moreover, some Prodi–Serrin type blow-up criteria are also established.