Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations

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On the well‐posedness of the Cauchy problem for an MHD system in Besov spaces (2006, background): “[ 3 ]), we can derive similarly by H¨older inequality”
Ill-posedness of the Navier-Stokes equations in a critical space in 3D (2008, background): “The problem is stated as a conjecture in [3] and [13].”
Well-posedness of the Cauchy problem for the fractional power dissipative equations (2006, background): “For more details see the example in [ 2 ]. We may also consider the well-posedness in the Besov space u B−� p,∞(R n ) of the problem (4.1).”
Weighted Norm Inequalities for Paraproducts and Bilinear Pseudodifferential Operators with Mild Regularity (2009, background): “Paraproducts have found plenty of inspired applications: from Bony’s paradifferential calculus (see [6]) and David–Journe’s remarkable T( 1)-theorem (see [16]) to their alliance with wavelet analysis in the study of PDEs (see, for instance, [8, 9 , 24, 43], and [44]) and their role as toy models or”
Well‐posedness for fractional Navier–Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn) (2012, background): “R3/, whose significance is due to the fact that it is the largest critical space in the sense that all other critical spaces are continuously embedded in it (see, e.g., Cannone [13], Frazier et al. [14], and Meyer [15]).”