Blow-up Criteria for the Three Dimensional Nonlinear Dissipative System Modeling Electro-hydrodynamics

Jihong Zhao; Meng Bai

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arXiv · 1509.06867

Blow-up Criteria for the Three Dimensional Nonlinear Dissipative System Modeling Electro-hydrodynamics

Jihong Zhao·Meng Bai

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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.

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Jihong Zhao, Meng Bai. 2015-09-23. Blow-up Criteria for the Three Dimensional Nonlinear Dissipative System Modeling Electro-hydrodynamics. https://arxiv.org/abs/1509.06867

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