Global infinite energy solutions of the critical semilinear wave equation

We consider the critical semilinear wave equation (Equation Presented) set in ℝ^d, d ≥ 3, with 2* = 2d/d-2. Shatah and Struwe [22] proved that, for finite energy initial data (ie if (u₀, u ₁) ∈ Ḣ¹ × L²), there exists a global solution such that (u, ∂_tu) ∈ C(ℝ, Ḣ¹ × L²). Planchon [17] showed that there also exists a global solution for certain infinite energy initial data, namely, if the norm of (u₀, u₁ ) in Ḃ_2,∞ ¹ × Ḃ_2,∞⁰ is small enough. In this article, we build up global solutions of (NLW)_2*-1 for arbitrarily big initial data of infinite energy, by using two methods which enable to interpolate between finite and infinite energy initial data: the method of Calderón, and the method of Bourgain. These two methods give complementary results.