Abstract
We consider the critical semilinear wave equation (Equation Presented) set in ℝd, 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 Ḃ2,∞ 1 × Ḃ2,∞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.
Original language | English (US) |
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Pages (from-to) | 463-497 |
Number of pages | 35 |
Journal | Revista Matematica Iberoamericana |
Volume | 24 |
Issue number | 2 |
DOIs | |
State | Published - 2008 |
Keywords
- Besov spaces
- Critical wave equation
- Global solutions
- Infinite energy
ASJC Scopus subject areas
- General Mathematics