Local wellposedness of the Vlasov‐Riesz‐Fokker‐Planck system in modulation space

We obtain local wellposedness for the Vlasov‐Riesz‐Fokker‐Planck system in Modulation space, as well as a regularity‐enhancing property of the system. We provide an estimate of the nonlinear term in Modulation space with higher regularity. The proof primarily relies on exploiting the properties of operators in Modulation space, while also drawing upon a proof analogous to that of the Bernstein multiplier theorem.