On the Cauchy Problem for the Cutoff Boltzmann Equation with Small Initial Data

We prove the global existence of non-negative unique mild solution for Cauchy problem cutoff Boltzmann equation soft potential model $$-1\le \gamma < 0$$ with small initial data in three dimensional space. Thus our result fixes gap case $$\gamma =-1$$ space authors’ previous work (He and Jiang J Stat Phys 168(2):470–481, 2017) where estimate loss term was improperly used. The other He (2017) =0$$ two is recently fixed by Chen et al. (Arch Ration Mech Anal 240:327–381, 2021). $$f_{0}$$ satisfies that $$\Vert \langle v \rangle ^{\ell _{\gamma }} f_{0}(x,v)\Vert _{L^{3}_{x,v}}\ll 1$$ f_0\Vert _{L^{15/8}_{x,v}}<\infty $$ $$\ell }=0$$ when }=(1+\gamma )^{+}$$ $$-1<\gamma <0$$ . also show scatters respect to kinetic transport operator. novel contribution this lies exploration symmetric property gain terms weighted estimate. It key ingredient solving applying Strichartz estimates.