Random Data Cauchy Theory for the Generalized Incompressible Navier–Stokes Equations

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On the Probabilistic Cauchy Theory of the Cubic Nonlinear Schrödinger Equation on Rd, d≥3 (2014, methodology): “PROBABILISTIC CAUCHY THEORY FOR THE CUBIC NLS ON Rd 51 [62] T. Zhang, D. Fang, Random data Cauchy theory for the generalized incompressible Navier-Stokes equations, J. Math.”
WIENER RANDOMIZATION ON UNBOUNDED DOMAINS AND AN APPLICATION TO ALMOST SURE WELL-POSEDNESS OF NLS (2014, methodology): “The randomization in [37] stems from yet another one used by Zhang and Fang [56] in their study of the Navier-Stokes equations.”
Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^d$, $d=4$ and $5$ (2014, unknown): “ener decomposition and modulation spaces. This seems to be quite canonical from the point of view of the time-frequency analysis [32]. Such a randomization was previously used in [42, 5, 6]. See also [68]. Given d≥ 1, let Qn be the unit cube Qn := n+ −1 2, 1 2 d centered at n∈ Zd. Then, consider the”