Semilinear hyperbolic systems with blowup at infinity Serge Alinhac 35L40energy inequalitynull conditionweak null conditionblowup at infinity We investigate semilinear hyperbolic systems in three-space dimensions with quadratic terms in gradient of the solution, not satisfying the null condition. Under some algebraic conditions ensuring global existence for solutions of the reduced systems (the so-called weak null condition of Lindblad and Rodnianski), we prove global existence of classical solutions for these systems. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2671 10.1512/iumj.2006.55.2671 en Indiana Univ. Math. J. 55 (2006) 1209 - 1232 state-of-the-art mathematics http://iumj.org/access/