Extended Strichartz estimates for the heat equation with a Strichartz type potential

摘要

We present new extended Strichartz estimates for the solutions to the heat equation, perturbed with a time dependent potential V : R_+ R~d → R, satisfying appropriate space and time integrability conditions (i.e. bounded with respect to some L~a(I, L_b(R~d)) norms). We focus ourselves to the case with initial datum in H~σ, σ ∈ (0, 1] and d ≥ 1. Some applications of these new estimates are also displayed.