Higher integrability for parabolic systems with Orlicz growth

We prove higher integrability of the spatial gradient of weak solutions to parabolic systems with $\varphi$-growth, where $\phi =\phi (t)$ is a general Orlicz function. The parabolic systems need be neither degenerate nor singular. Our result is a generalized version of the one of J. Kinnunen and J. Lewis [Duke Math. J. 102 (2000), no. 2, 253–271] for the parabolic $p$-Laplace systems.