On global solutions to a defocusing semi-linear wave equation

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Invariant measure for a three dimensional nonlinear wave equation (2007, unknown): “Such a regularity seems to be out of reach of the present deterministic methods (see in the case of a cubic non linearity on R3 the related works by Bourgain [5], Kenig, Ponce, Vega [10], Gallagher, Planchon [8] and Bahouri, Chemin [2]).”
Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ3 (2014, background): “1) for 2 ≤ < 5 for initial data in a range of sub-critical spaces below the energy space (see also [1, 16, 34] for = 3).”
Scattering for the radial 3D cubic wave equation (2014, background): “There has been a good deal of recent work extending the local existence result of Lindblad and Sogge [1995] in H s × H s−1 for s > (1)2 to an unconditional global well-posedness result, and we refer the reader to [Kenig et al. 2000; Gallagher and Planchon 2003; Bahouri and Chemin 2006; Roy 2009] and”
Probabilistic well-posedness for the cubic wave equation (2011, unknown): “In this section, we are going to follow the high-low decomposition method of Bourgain [6], or more precisely the reverse of Bourgain’s method, as developed for instance in the work by Gallagher and Planchon [15] (see also [19]) or Bona and the second author [2] and refine the global well-posedness r”