GLOBAL WELL-POSEDNESS FOR THE DISSIPATIVE SYSTEM MODELING ELECTRO-HYDRODYNAMICS WITH LARGE VERTICAL VELOCITY COMPONENT IN CRITICAL BESOV SPACE

摘要

In this paper, we are concerned with a model arising from electro-hydrodynamics, which is a coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. The local well-posedness and global well-posedness with small initial data to the 3-D Cauchy problem of this system are established in the critical Besov space B_(p,1)~(-1+3/p) (R~3) x (B_(q,l) ~(-2+3/q) (R~3))~2 with suitable choices of p, q. Especially, we prove that there exist two positive constants c_o,C_o depending on the coefficients of system except μ such that if then the above local solution can be extended to the global one. This result implies the global well-posedness of this system with large initial vertical velocity component.