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We study the slightly perturbed homogeneous Landau equation \[ \partial_t f =a_{ij}(f) \cdot \partial_{ij} f + \alpha c(f) f, \quad c(f) = - \partial_{ij}a_{ij}(f), \] with very soft potentials, where we increase the nonlinearityfrom $ c(f) f$ in the Landau equation to $\alpha c(f) f$ with $\alpha>1$. For$\alpha > 1 $ and close to $1$, we establish finite time nearly self-similarblowup from some smooth initial data $f_0 \geq 0$, which can be both radiallysymmetric or non-radially symmetric. The blowup results are sharp as thehomogeneous Landau equation $(\alpha=1)$ is globally well-posed, which wasestablished recently by Guillen and Silvestre. To prove the blowup results, webuild on our previous framework \cite{chen2020slightly,chen2021regularity} onsharp blowup results of the De Gregorio model with nearly self-similarsingularity to overcome the diffusion. Our results shed light on potentialsingularity formation in the inhomogeneous setting.

Nearly self-similar blowup of the slightly perturbed homogeneous Landau equation with very soft potentials