Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

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Global existence and decay of solutions to Prandtl system with small analytic data. (2019, unknown): “In order to overcome the difficulty that one can not use Gronwall’s type argument in the framework of Chemin-Lerner space L̃(2)T (Bs,0), we also need to use the time-weighted CheminLerner type norm, which was introduced by the authors in [20].”
Global small solutions to 2-D incompressible MHD system (2013, unknown): “It also suggests us to employ the tool of anisotropic Littlewood-Paley theory, which has been used in the study of the global wellposedness to 3D anisotropic incompressible Navier-Stokes equations [7, 8, 18, 19, 28, 29, 33], and in [25] to explore the dissipative properties to the three-dimensional ”
Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system (2012, methodology): “Motivated by [19,23,15] concerning the global well-posedness of 3-D incompressible anisotropic Navier–Stokes system with the third component of the initial velocity field being large, we are going to relax the smallness condition in Theorem 1.”
Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case (2014, methodology): “9) may be more complicated than that for the linearized system of the isentropic compressible Navier-Stokes system in [8], and this brief analysis also suggests to us to employ the tool of anisotropic Littlewood-Paley theory, which has been used in the study of the anisotropic incompressible NavierS”