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Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups
We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form $L^\infty+M^q_K$ force field which can produce local blow-ups due to strong attraction to a submanifold. Our approach is based on the fractional representation for the Duhamel series of the equation
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