Global well-posedness and ill-posedness for the Navier–Stokes equations with the Coriolis force in function spaces of Besov type

Babin, 1997, Regularity and integrability of 3D Euler and Navier–Stokes equations for rotating fluids, Asymptot. Anal., 15, 103, 10.3233/ASY-1997-15201 Babin, 1999, Global regularity of 3D rotating Navier–Stokes equations for resonant domains, Indiana Univ. Math. J., 48, 1133 Babin, 2001, 3D Navier–Stokes and Euler equations with initial data characterized by uniformly large vorticity, Indiana Univ. Math. J., 50, 1, 10.1512/iumj.2001.50.2155 Bejenaru, 2006, Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation, J. Funct. Anal., 233, 228, 10.1016/j.jfa.2005.08.004 Bony, 1981, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. Ec. Norm. Super. (4), 14, 209, 10.24033/asens.1404 Bourgain, 2008, Ill-posedness of the Navier–Stokes equations in a critical space in 3D, J. Funct. Anal., 255, 2233, 10.1016/j.jfa.2008.07.008 Chemin, 2002, Anisotropy and dispersion in rotating fluids, Stud. Math. Appl., 31, 171, 10.1016/S0168-2024(02)80010-8 Chemin, 2006 Christ, 1991, Dispersion of small amplitude solutions of the generalized Korteweg–de Vries equation, J. Funct. Anal., 100, 87, 10.1016/0022-1236(91)90103-C Fujita, 1964, On the Navier–Stokes initial value problem. I, Arch. Ration. Mech. Anal., 16, 269, 10.1007/BF00276188 Germain, 2008, The second iterate for the Navier–Stokes equation, J. Funct. Anal., 255, 2248, 10.1016/j.jfa.2008.07.014 Giga, 2005, Uniform local solvability for the Navier–Stokes equations with the Coriolis force, Methods Appl. Anal., 12, 381, 10.4310/MAA.2005.v12.n4.a2 Giga, 2006, Navier–Stokes equations in a rotating frame in R3 with initial data nondecreasing at infinity, Hokkaido Math. J., 35, 321, 10.14492/hokmj/1285766360 Giga, 2008, Uniform global solvability of the rotating Navier–Stokes equations for nondecaying initial data, Indiana Univ. Math. J., 57, 2775, 10.1512/iumj.2008.57.3795 Hieber, 2010, The Fujita–Kato approach to the Navier–Stokes equations in the rotational framework, Math. Z., 265, 481, 10.1007/s00209-009-0525-8 Iwabuchi, 2011, Global well-posedness for Keller–Segel system in Besov type spaces, J. Math. Anal. Appl., 379, 930, 10.1016/j.jmaa.2011.02.010 Kato, 1984, Strong Lp-solutions of the Navier–Stokes equation in Rm, with applications to weak solutions, Math. Z., 187, 471, 10.1007/BF01174182 Koch, 2001, Well-posedness for the Navier–Stokes equations, Adv. Math., 157, 22, 10.1006/aima.2000.1937 Konieczny, 2011, On dispersive effect of the Coriolis force for the stationary Navier–Stokes equations, J. Differential Equations, 250, 3859, 10.1016/j.jde.2011.01.003 Kozono, 2004, Bilinear estimates in homogeneous Triebel–Lizorkin spaces and the Navier–Stokes equations, Math. Nachr., 276, 63, 10.1002/mana.200310213 Kozono, 1994, Semilinear heat equations and the Navier–Stokes equation with distributions in new function spaces as initial data, Comm. Partial Differential Equations, 19, 959, 10.1080/03605309408821042 Yoneda, 2010, Ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space near BMO−1, J. Funct. Anal., 258, 3376, 10.1016/j.jfa.2010.02.005 Yoneda, 2011, Long-time solvability of the Navier–Stokes equations in a rotating frame with spatially almost periodic large data, Arch. Ration. Mech. Anal., 200, 225, 10.1007/s00205-010-0360-4