Department of Mathematics - SEMINAR ON PDE - Finite energy solutions to the 6D Fujita equation in the
Sobolev critical case

We discuss the dynamics near the ground states for the 6D Fujita equation. This result
presents a 6D version of the classification in a higher dimensional setting, obtained by
Charles Collot - Frank Merle - Pierre Raphael (2017). In contrast to their results (they assume
only that 𝑢! ∈ 𝐻̇"(𝑅#)), our result requires the additional integrability conditions on the
initial data𝑢! ∈ 𝐿$(𝑅#). We also point out that the assumption 𝑢! ∈ 𝐻̇"(𝑅#) alone is not
sufficient for the stabilization of the solution in the case 𝑛 = 6.