Ibrahim, Slim; Majdoub, Mohamed Solutions globales de l’équation des ondes semi-linéaire critique à coefficients variables. (Global solutions for the critical nonlinear wave equation in variable coefficients). (French) Zbl 1024.35077 Bull. Soc. Math. Fr. 131, No. 1, 1-22 (2003). Summary: In this work, we study the existence of both global smooth and Shatah-Struwe’s solutions of the critical wave equation in variable coefficients in dimension \(d\) of space \[ \square_Au+ u ^{{4}/{(d-2)}}u=\partial^2_t u- \text{div}(A(x)\cdot \nabla_xu)+ u ^{{4}/{(d-2)}}u=0,\quad \mathbb{R}_t\times \mathbb{R}^d_x, \] where \(A\) is a regular function valued in the space of \(d\times d\) positive definite matrix and which is the identity outside a fixed compact. Cited in 8 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35B33 Critical exponents in context of PDEs Keywords:Strichartz estimates; geodesic cones PDFBibTeX XMLCite \textit{S. Ibrahim} and \textit{M. Majdoub}, Bull. Soc. Math. Fr. 131, No. 1, 1--22 (2003; Zbl 1024.35077) Full Text: DOI