In this paper, we prove quasi-global existence (resp. global existence) for quasilinear wave equations in two space dimensions satisfying the null condition (resp. both null conditions). In contrast with the case of three space dimensions where the result, due to D. Christodoulou and S. Klainerman, has been known since 1986, this problem has remained open until now, except for the special cases of cubic terms or rotationally invariant equations. Our proof relies on the construction of an approximate solution, combined with an energy integral method which displays the null condition(s).
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