Global well-posedness for the 3D rotating fractional Boussinesq equations in Fourier-Besov-Morrey spaces with variable exponent

Abstract

This paper considers the Cauchy problem of the 3D rotating fractional Boussinesq equations in Fourier-Besov-Morrey spaces with variable exponent. By using the contraction mapping method, Littlewood-Paley theory and the Fourier localization argument, we get, with small initial data in the critical Fourier-Besov-Morrey spaces with variable exponent FN_(r(·),q(·),h)^(4 - 2β - 3/r(·) ), the global well-posedness result.