References
- H. Bahouri, J.Y. Chemin and R. Danchin. Fourier Analysis and Nonlinear Partial Differential Equations. Grundlehren Math. Wiss.. Springer, 2011.
- J.M. Bony. Calcul symbolique et propagation des singularités pour équations aux dérivées partielles nonlinéaires. Ann. Sci. École Norm. Sup., 14: 209–246, 1981.
- J.Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier. Anisotropy and dispersion in rotating fluids. Stud. Math. Appl., 31: 171–192, 2002. http://dx.doi.org/10.1016/S0168-2024(02)80010-8.
- J.Y. Chemin and N. Lerner. Flot de champs de vecteurs non Lipschitziens et équations de Navier–Stokes. J. Differential Equations, 121: 314–228, 1995. http://dx.doi.org/10.1006/jdeq.1995.1131.
- D. Fang and Z. Zi. Rui. On the well-posedness of inhomogeneous hyperdissipative Navier–Stokes equations. Discrete Contin. Dyn. Syst., 33: 3517–3541, 2013. http://dx.doi.org/10.3934/dcds.2013.33.3517.
- D. Iftimie. The resolution of the Navier–Stokes equations in anisotropic spaces. Rev. Mat. Iberoamericana, 15: 1–36, 1999. http://dx.doi.org/10.4171/RMI/248.
- N. Katz and N. Pavlović. A cheap Caffarelli–Kohn–Nirenberg inequality for the Navier–Stokes equaiton with hyper-dissipation. Geom. Funct. Anal., 12: 355–379, 2002. http://dx.doi.org/10.1007/s00039-002-8250-z.
- M. Majdoub and M. Paicu. Uniform local existence for inhomogeneous rotating fluid equations. J. Dynam. Differential Equations, 21: 21–44, 2009. http://dx.doi.org/10.1007/s10884-008-9120-7.
- M. Paicu. Equation periodique de Navier–Stokes sans viscosite dans une direction. Comm. Partial Differential Equations, 30: 1107–1140, 2005. http://dx.doi.org/10.1080/036053005002575529.
- T. Tao. Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equation. Anal. PDE, 22: 361–366, 2009. http://dx.doi.org/10.2140/apde.2009.2.361.
- T. Zhang. Global wellposed problem for the 3-d incompressible anisotropic Navier–Stokes equations in an anisotropic space. Commun. Math. Phys., 287: 211–224, 2009. http://dx.doi.org/10.1007/s00220-008-0631-1.