Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

[1] H.Bahouri, J.-Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, Vol. 343. New York: Springer- Verlag (2011).10.1007/978-3-642-16830-7Search in Google Scholar

[2] Y.Baoquan, and J.Yuan, Global well-posedness of incompressible ow in porous media with critical diffusion in Besov spaces. Journal of Differential Equations 246.11 (2009):4405-4422.10.1016/j.jde.2009.01.022Search in Google Scholar

[3] Q.Bie, Q.Wang, and Z.A.Yao. On the well-posdness of the inviscid Boussinesq equations in the Besov-Morrey spaces. Kinetic Related Models 8.3 (2015).10.3934/krm.2015.8.395Search in Google Scholar

[4] M. Cannone, A generalization of a theorem by Kato on Navier-Stokes equations , Revisit Matematica IberoAmericana, 13, 3, 199710.4171/RMI/229Search in Google Scholar

[5] M. Cannone, Ondelettes, Paraproduits et Navier-Stokes, Diderot Editeur, 1995.Search in Google Scholar

[6] M. Cannone and G. Wu, Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces, Nonlinear Anal., 75 (2012)10.1016/j.na.2012.01.029Search in Google Scholar

[7] L.C.Ferreira, and L.S.Lima, Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces. Monatsh. Math. 175.4 (2014): 491-509.10.1007/s00605-014-0659-6Search in Google Scholar

[8] E. Hopf, Über die Anfangswertaufgabe für die hydrodinamischen Grundgleichungen, Math. Nach., 4, pages 213-231, 1951.10.1002/mana.3210040121Search in Google Scholar

[9] T.Kato, Nonstationary flows of viscous and ideal uids in R3, J. Funct. Anal., 9 (1972), 296-305.10.1016/0022-1236(72)90003-1Search in Google Scholar

[10] T.Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Mathematics, 448, Springer-Verlag, pages 25-70, 1975.10.1007/BFb0067080Search in Google Scholar

[11] T. Kato, Strong LP solutions of the Navier-Stokes equations in Rm, with applications to weak solutions, Math. Z., 187 : 4(1984); 471 - 480.10.1007/BF01174182Search in Google Scholar

[12] T.Kato, Strong solutions of the Navier-Stokes equations in Morrey spaces. Bol. Soc. Brasil Mat. 22(2), 127155, 1992.10.1007/BF01232939Search in Google Scholar

[13] T. Kato and H. Fujita,On the Navier-Stokes initial value problem I, Arch. Ration. Mech. Anal., 16(1964); 269 - 35110.1007/BF00276188Search in Google Scholar

[14] H. Koch and D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math., 157:1 (2001), 22-35.10.1006/aima.2000.1937Search in Google Scholar

[15] Z.Lei and F. Lin, Global mild solutions of Navier-Stokes equations, Comm. Pure Appl. Math., 64:9 (2011)10.1002/cpa.20361Search in Google Scholar

[16] P.G. Lemarié-Rieusset, The Navier-Stokes Problem in the 21st Century, CRC Press 2016.10.1201/b19556Search in Google Scholar

[17] J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math.1934, vol. 63, no 1, p. 193-248.Search in Google Scholar

[18] R.May, and E.Zahrouni, Existence of global solutions to the 2-D subcritical dissipative quasigeostrophic equation and persistency of the initial regularity. Electronic Journal of Differential Equations 2011.08 (2011): 1-18.Search in Google Scholar

[19] W. Sickel, Smoothness spaces related to Morrey spaces -a survey. I, Eurasian Math. J., 2012, Volume 3, Number 3, 110-149Search in Google Scholar

[20] M.E.Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Commun. Partial Differ. Equ. 17, 1407-1456, 1992.10.1080/03605309208820892Search in Google Scholar

[21] W.Xiao, J.Chen, D.Fan,and X.Zhou,Global Well-Posedness and Long Time Decay of Fractional Navier-Stokes Equations in Fourier Besov Spaces. In Abstract and Applied Analysis (Vol. 2014). Hindawi Publishing Corporation.10.1155/2014/463639Search in Google Scholar

[22] W. Yuan, W. Sickel, and D. Yang, Morrey and Campanato Meet Besov, Lizorkin and Triebel, vol. 2005 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010. Search in Google Scholar