| Abstract: |
| Even in the spatially homogeneous case, any Maxwellian upper bound for the Boltzmann solution must be characterized by an exceptionally small decay rate in the velocity variable. This motivates us to study the Boltzmann equation with a stretched exponential weight, $e^{-\alpha|v|^\kappa}$ for $\kappa < 2$. In this talk, we discuss the well-posedness of the Boltzmann equation in $L^\infty_{x,v}$ within this stretched exponential framework. In particular, we address the large-amplitude problem of the Boltzmann equation and beyond. |
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