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In this paper, we consider the global well-posedness to the non-cutoffBoltzmann equation with soft potential in the $L^\infty$ setting. We show thatwhen the initial data is close to equilibrium and the perturbation is small in$L^2 \cap L^\infty$ polynomial weighted space, the Boltzmann equation has aglobal solution in the weighted $L^2 \cap L^\infty$ space. The ingredients ofthe proof lie in strong averaging lemma, new polynomial weighted estimate forthe non-cutoff Boltzmann equation and the $L^2$ level set Di Giorgi iterationmethod developed in \cite{AMSY2}. The convergence to the equilibrium state inboth $L^2$ and $L^\infty$ spaces is also proved.

De Giorgi Argument for non-cutoff Boltzmann equation with soft potentials