  In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates
for gradients of solutions to the quasilinear parabolic equations:
$$u_t-\operatorname{div}(A(x,t,\nabla u))=\operatorname{div}(F),$$ in a bounded
domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$, under minimal regularity
assumptions on the boundary of domain and on nonlinearity $A$. Then results
yields existence of a solution to the Riccati type parabolic equations:
$$u_t-\operatorname{div}(A(x,t,\nabla u))=|\nabla
u|^q+\operatorname{div}(F)+\mu,$$ where $q>1$ and $\mu$ is a bounded Radon
measure.
