Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation

Probabilistic well-posedness for the nonlinear wave equation on $ B_2\times\mathbb{T} $

“…In [16], Colliander and Oh studied NLS on T at low regularity, and made use of a probabilistic local theory as part of their arguments. For NLW on the flat 3D torus T 3 , Burq and Tzvetkov have obtained probabilistic global well-posedness results [15], using a variety of energy-based considerations; further results in this direction are due to Pocovnicu [24], Oh-Pocovnicu [21], Lührmann-Mendelson [19], Sun-Xia [27], and Oh-Pocovnicu-Tzvetkov [22]; see also [9,10]. We also mention [20] for results concerning the Navier-Stokes system.…”

“…Estimates of the nonlinearity. In this section we establish two lemmas which will provide estimates for the nonlinear term of the Duhamel formula (10). These lemmas, when combined with the probabilistic bounds of Section 3, will facilitate the proof of the local well-posedness result stated in Theorem 1.1 by allowing us to close a contraction mapping argument in suitable X s,b norms.…”