Optimal well-posedness and forward self-similar solution for the Hardy–Hénon parabolic equation in critical weighted Lebesgue spaces

The Cauchy problem for the Hardy–Hénon parabolic equation is studied in critical and subcritical weighted Lebesgue spaces on Euclidean space R d . In earlier works, well-posedness of singular initial data existence non-radial forward self-similar solutions to were shown Hardy Fujita cases ( ? ? 0 ). are used treat potential | x as an increase or decrease weight, which enables us prove all , with ? min { 2 } < including Hénon case > As a by-product global existence, established without restrictions. Furthermore, non-existence local solution supercritical also shown. Therefore, our exponent, s c optimal regard solvability.