In this short note, we prove that Formula: see text-concavity of the pressure is not preserved for the porous medium equation in dimensions Formula: see text and higher for any Formula: see text. Together with the result of Chau-Weinkove for Formula: see text, this fully resolves an open problem posed by Vásquez on whether pressure concavity is preserved in general for the porous medium equation.
Shen et al. (Fri,) studied this question.