Advanced Nonlinear Studies (Aug 2018)
Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Abstract
This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the solutions are analytic for a small interval of time with values in a Gevrey class of functions. As a consequence of Gevrey estimates, we particularly imply higher-order derivatives of solutions in Besov and Lebesgue spaces. Moreover, we prove that the existence of a positive constant C~{\tilde{C}} such that the initial data (u0,n0,c0):=(u0h,u03,n0,c0){(u_{0},n_{0},c_{0}):=(u_{0}^{h},u_{0}^{3},n_{0},c_{0})} satisfy
Keywords