Higher integrability for parabolic PDEs with generalized Orlicz growth

We prove higher integrability of the gradient of weak solutions to nonlinear parabolic systems whose prototype is \[ \partial_t u-\mathrm{div}\Big(\frac{φ'(z, |\nabla u|)}{|\nabla u|}\nabla u\Big) =0, \qquad u=(u^1,\dots,u^N), \] where $φ$ is a generalized Young function. Special cases of our main t