Global stability of solutions to nonlinear wave equations

We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution, which guarantees stability. Our stability result can be reduced to a small data global existence result for a class of semilinear wave equations with linear terms , and quadratic terms where the functions , , decay rather weakly and the constants satisfy the null condition. We show the small data global existence result by using the new approach developed by Dafermos-Rodnianski. In particular, we prove the global stability result under weaker assumptions than those imposed by Alinhac (Indiana Univ Math J 58(6):2543-2574, 2009).