  It is well-known that in dimensions at least three semilinear wave equations
with null conditions admit global solutions for small initial data. It is also
known that in dimension two such result still holds for a certain class of
quasi-linear wave equations with null conditions. The proofs are based on the
decay mechanism of linear waves. However, in one dimension, waves do not decay.
Nevertheless, we will prove that small data still lead to global solutions if
the null condition is satisfied.
