Algebra Properties in Fourier-Besov Spaces and Their Applications. (4th December 2018) - Zhou, Xuhuan; Xiao, Weiliang
Abstract : We estimate the norm of the product of two scale functions in Fourier-Besov spaces. As applications of these algebra properties, we establish the global well-posedness for small initial data and local well-posedness for large initial data of the generalized Navier-Stokes equations. Particularly, we give a blow-up criterion of the solutions in Fourier-Besov spaces as well as a space analyticity of Gevrey regularity.