Fluids with anisotropic viscosity

By Jean-Yves Chemin, B. Desjardins, Isabelle Gallagher, E. Grenier. 2000

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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 Small Solutions to an MHD‐Type System: The Three‐Dimensional Case (2014, methodology): “9), instead of using the classical anisotropic-type Besov spaces as found in [5, 6, 10, 17], we need to introduce the following norm: DEFINITION 2.”
Localization in Fourier space and Navier-Stokes system (2005, unknown): “The study of anisotropic incompressible Navier-Stokes system has been initiated in [13] and in [35].”
GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO (2008, background): “For the standard three-dimensional incompressible Navier-Stokes equations, the first mathematical results concerning anisotropic viscosity have been obtained in [10, 22].”