For linear Boltzmann transport problems whose data vanish on the inflow and characteristic boundary parts, strong solutions exist with arbitrary spatial Sobolev regularity, including with a continuous slowing-down energy term.
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On existence of spatially regular strong solutions for a class of transport equations
For linear Boltzmann transport problems whose data vanish on the inflow and characteristic boundary parts, strong solutions exist with arbitrary spatial Sobolev regularity, including with a continuous slowing-down energy term.