Communications in Mathematical Sciences
Volume 17 (2019)
The 3D nonlinear dissipative system modeling electro-diffusion with blow-up in one direction
Pages: 131 – 147
This paper establishes a sufficient condition for the breakdown of local smooth solutions, to the Cauchy problem of the 3D Navier–Stokes/Poisson–Nernst–Planck system modeling electro-diffusion, via one directional derivative of the horizontal component of the velocity field (i.e., $(\partial_i u_1 , \partial_j u_2 , 0)$ where $i, j \in \lbrace 1,2,3 \rbrace)$ in the framework of the anisotropic Lebesgue spaces.
Navier–Stokes/Poisson–Nernst–Planck system, blow-up, anisotropic Lebesgue spaces
2010 Mathematics Subject Classification
35B44, 35K55, 35Q35, 76W05
This paper is partially supported by the National Natural Science Foundation of China (11401202), and by the China Postdoctoral Science Foundation (2015M570053, 2016T90063).
Received 7 May 2018
Accepted 19 October 2018
Published 30 May 2019