In this article, for 0 ≤ 𝑚 < ∞ and the index vectors 𝑞 = (𝑞1,𝑞2 ,𝑞3),𝑟 = (𝑟1,𝑟2,𝑟3) where 1 ≤ 𝑞𝑖 ≤ ∞,1 < 𝑟𝑖 < ∞ and 1 ≤ 𝑖 ≤ 3, we study new results of Navier-Stokes equations with Coriolis force in the rotational framework in mixed-norm Sobolev–Lorentz spaces 𝐻̇ 𝑚,𝑟,𝑞(𝑅3), which are more general than the classical Sobolev spaces. We prove the existence and uniqueness of solutions to the Navier–Stokes equations (NSE) under Coriolis force in the spaces 𝐿∞([0, T]; 𝐻̇ 𝑚,𝑟,𝑞 ) by using topological arguments, the fixed point argument and interpolation inequalities. Our work is based on the paper [2] and extend some results of it to gain new results of the Navier-Stokes equations in rotational framework
