GEVREY REGULARITY AND EXISTENCE OF NAVIER-STOKES-NERNST-PLANCK-POISSON SYSTEM IN CRITICAL BESOV SPACES

The paper deals with the Cauchy problem of Navier-Stokes-NernstPlanck-Poisson system (NSNPP). First of all, based on so-called Gevrey regularity estimates, which is motivated by the works of Foias and Temam [J. Funct. Anal., 87 (1989), 359-369], we prove that the solutions are analytic in a Gevrey class of functions. As a consequence of Gevrey estimates, we particularly obtain higher-order derivatives of solutions in Besov and Lebesgue spaces. Finally, we prove that there exists a positive constant C such that if the initial data (u(0), n(0), c(0)) = (u(0)(h), u(0)(3), n0, c0) satisfies parallel to(n(0),c(0),u(0)(h))parallel to (B) over dot(q,1)(-2+3/q) x (B) over dot(q,1)(-2+3/q) x (B) over dot(p,1)(-1+3/p) + parallel to u(0)(h)parallel to(alpha)(-1+3/p)((B) over dotp,1) parallel to u(0)(3)parallel to(1-alpha)(-1+3/p)((B) over dotp,1) <= 1/C for p, q, alpha with 1 < p < q <= 2p < infinity, 1/p + 1/q > 1/3, 1 < q < 6, 1/p - 1/q <= 1/3, then global existence of solutions with large initial vertical velocity component is established.