On the well-posedness in Lorentz spaces for the inhomogeneous heat equation.

We present new Strichartz estimates in Lorentz spaces for the solutions to the heat equation with inhomogeneous nonlinearity in the mass subcritical framework and space dimension d ≥ 1. As an application we prove local and global well-posedness in the Strichartz-Lorentz space Lq((0, T); Lr,2(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the L2(ℝd) space. [ABSTRACT FROM AUTHOR]