[1]Institut de Mathematiques de Bordeaux Universite Bordeaux 1 Talence 33405 France;
[2]Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing 100190 China;
[3]School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China;
anisotropic Navier-Stokes equations; Littlewood-Paley theory; well-posedness;