中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (3): 140-144.doi: 10.13471/j.cnki.acta.snus.2019.03.017

• 论文 • 上一篇    下一篇

三维耗散型电流体动力学系统在齐次 Triebel-Lizorkin空间中的BKM型爆破准则

李秀蓉, 梁洪   

  1. 西北农林科技大学理学院,陕西 杨凌 712100
  • 收稿日期:2018-07-29 出版日期:2019-05-25 发布日期:2019-05-25
  • 通讯作者: 李秀蓉 (1994年生),女;研究方向:偏微分方程;E-mail:CherryXR@126.com

BKMs blowup criterion in homogeneous Triebel-Lizorkin spaces for the 3D dissipative system in electrohydrodynamics

LI Xiurong,LIANG Hong   

  1. College of Science, Northwest A&F University, Yangling 712100, China
  • Received:2018-07-29 Online:2019-05-25 Published:2019-05-25

摘要:

非线性耗散型电流体动力学系统局部光滑解的爆破问题由流体力学中的不可压Navier-Stokes方程和电动力学的Poisson-Nernst-Planck方程强耦合而成,主要刻画等温不可压粘性流体中带电离子的漂移、扩散和对流现象。基于Littlewood-Paley分解理论,建立了该系统局部光滑解在齐次Triebel-Lizorkin空间中与速度场水平分量相关的BKM型爆破准则,推广了之前结果。特别地,该爆破准则指出,在研究解的爆破问题中,速度场水平分量比带电粒子密度函数更具重要性。

关键词: 电流体动力学系统, Navier-Stokes方程, Poisson-Nernst-Planck方程, Triebel-Lizorkin空间, 爆破准则

Abstract:

In this paper, we study the breakdown of local smooth solutions for a class of nonlinear dissipative electro-hydrodynamics system. This system is a strongly coupled system by the well-known incompressible Navier-Stokes equations in hydromechanics and Poisson-Nernst-Planckequations in electrodynamics, modeling the drift, diffusion and convection phenomena of charged particle in an isothermal, incompressible and viscous fluids. Based on the Littlewood-Paley decomposition theory, the BKM's blowup criterion in terms of horizontal component of velocity field in homogeneous Triebel-Lizorkin spaces is established for local smooth solutions, and generalize the previous results. In particular, this blowup criterion reveals that the horizontal component of velocity field is more important than the density functions of charged particles in the blow-up theory of the system.

Key words: electro-hydrodynamics system, Navier-Stokes equations; Poisson-Nernst-Planck equations, Triebel-Lizorkin spaces, blowup criterio

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