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In this paper, the global well-posedness of semirelativistic equations with apower type nonlinearity on Euclidean spaces is studied. In two dimensional$H^s$ scaling subcritical case with $1 \leq s \leq 2$, the local well-posednessfollows from a Strichartz estimate. In higher dimensional $H^1$ scalingsubcritical case, the local well-posedness for radial solutions follows from aweighted Strichartz estimate. Moreover, in three dimensional $H^1$ scalingcritical case, the local well-posedness for radial solutions follows from auniform bound of solutions which may be derived by the corresponding onedimensional problem. Local solutions may be extended by a priori estimates.

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