Abstract:  In this paper,we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations …. We proved that the range of s is ,respectively,with if  n=2, and δ>0 if n=3, and δ≥0 if n≥4. Which  is  consistent   with  Lindblad's  counterexamples [3] for n=3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.

Key words: semilinear wave equations, local existence, low regularity