Boltzmann Equation and Hard Sphere Gas with Singular Initial Data: Well-posedness, Kinetic Limit, and Weak Stability

We develop a local well-posedness theory for the spatially inhomogeneous 3-d Boltzmann equation with hard sphere cross-section, accommodating a class of large initial data. This class is an interpolation between the space $L_{x}^{\infty}L_v^{1}$ and $L_{v}^1L_{x}^{\infty}$ (with weight in $v$). It i