On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases

In this paper, the global well-posedness of semirelativistic equations with a power type nonlinearity on Euclidean spaces is studied. In two dimensional H^s scaling subcritical case with 1≤s≤2, the local well-posedness follows from a Strichartz estimate. In higher dimensional H¹ scaling subcritical case, the local well-posedness for radial solutions follows from a weighted Strichartz estimate. Moreover, in three dimensional H¹ scaling critical case, the local well-posedness for radial solutions follows from a uniform bound of solutions which may be derived by the corresponding one dimensional problem. Local solutions may be extended by a priori estimates.